Assuming you have a line of sight to all your flashes and both methods will trigger the flashes with 100% reliability, is it faster to use radio triggers or optical triggers to set them off? Or put in other words, how does the delay time for radio triggers compare to optical triggers, and does the delay, if any, have an appreciable effect on photos?
Good radio wireless remotes, like PocketWizards, fire extremely fast, well within the time the shutter opens; I pushed mine a long ways past 1/1000 before I saw problems with a black bar beginning to creep into the image.
I think they're both adequate for normal situations. It's when you get into adverse situations that you'll see one work better than the other.
If you're in an area with a lot of radio/electromagnetic noise or need to shoot through a metal mesh fence an optical trigger will probably blow away the radio trigger.
If you're not line of sight, or dealing with dust, rain, snow or fog or at a distance that the optical can't cover, then radio triggers will win.
I have PocketWizard remote triggers because I needed something to work in really lousy conditions outdoors. I've used them in the rain, dust, heat, cold, up in grandstands, running all over the place, without needing to worry whether I was where the trigger could see me.
I think reliable triggering for your shooting conditions is the most important thing, over speed or whether it's radio or optical.
Your question is what's FASTER, radio or optical?; the answer is that it depends on the trigger more than the mechanism. Radio waves and light are essentially the same thing and therefore travel at the same speed.
Radio triggers include more circuitry and processing since they often accept multiple channels, etc. PocketWizard advertises that the response time of their MultiMax trigger is as low as 1/3000th of a second, due to their "ultrafast microprocessors". I had a hard time finding solid data on the response time of a typical "dumb" optical slave (like a Wein), but I saw commentary on it ranging from 0.1 sec to just 1-2ms. So, in spite of the additional electronics it would seem that the radio option will be faster, but surely this depends a lot on what type of photodiode/resistor is being used in the trigger.
All that said, none of this likely matters unless you are attempting to capture something that happens incredibly fast and without warning.
Typically in high-speed photography applications you are triggering a flash pulse based on some event; often either sound or interruption of a beam of light. Given that, you should be able to compensate for the 0.3ms delay of a PocketWizard simply by subtracting that time from your trigger... That'd be a matter of dialing it in if you're using something fancy, or if you're using a light/sound-based system just move the trigger ever-so-slightly closer to your subject.
For example, if you're triggering a flash based on the sound of a balloon popping, moving the microphone closer to the balloon will cause the flash to fire sooner since the sound has less distance to travel. Sound being slow (relative to light), you wouldn't need to move it very far to make up for 1/3000th of a second... maybe a few inches?
The second part of your question, will it have an appreciable effect on photos?... Most likely not, since it isn't the response time of the trigger that makes the image but rather it's the duration of the flash itself.
Optical slaves are considerably quicker - easily measured with a 'scope. Radio slaves offer longer range and more varied working conditions - unaffected by bright light and so on.
Good radio slaves introduce a delay of around 600 microseconds (0.6 milliseconds), some are slower - I measured mine at 1.2ms, which surprised me (it was longer than I expected). Still, even with that delay, I only have to drop the D700 down to 1/200 to get rid of any black bars. (at 1/200 sec, the shutter is open for 1ms longer than at 1/250, and the D700 is actually good for 1/320 sync with a hardwired flash.)
Optical slaves will introduce under a tenth of that delay, of the order of 60 microseconds, and may be regarded as more or less instant in practical terms in most situations. You can mix radio and optical triggers without worrying about the extra delay - e.g. trigger a distant flash by radio, and have it trigger several flashes near it optically, at worst you might have to drop back to 1/160 sec shutter speed on one of the modern cameras, but probably not.
Optical trigger which are trying to eliminate metering pre-flashes etc. might well introduce other delays, but simple "dumb" photodiode triggers are quick. Optical triggers which understand the pre-flash protocol properly for e.g. Canon's ETTL or Nikon's iTTL will be able to trigger at the correct point for all supported shutter speeds, obviously. So my Yongnuo 568EX flashes, optically triggered, will work at all shutter speeds (switching seamlessly to FP mode for speeds faster than 1/320) and my manual Yongnuo 560-II will optically sync up to 1/320 without banding, but, when the camera's in iTTL commander mode, simply refuses to fire at faster speeds (as that flash doesn't do FP sync, but seems to understand enough of the preflash protocol to know not to fire.)
This was of some interest to me because I have been getting the horizontal bars, so I did a lot of research and some testing. My camera has a nominal sync speed of 1/200 and I am using Britek PS-200 and PS-250 strobes which have a flash duration of 1/1500s. My interest was because I noticed a significant difference when firing just one strobe with a radio trigger and using the built-in optical slaves on the others against having radio receivers on all of the strobes.
I did some testing and worked out that my curtain speed (the time from the curtain starting its travel to the time it finishes) is about 3.7ms, which allows just 1.3ms of the shutter being fully open for the flash to trigger, at a shutter speed of 1/200, before the rear curtain starts moving. I'm assuming that the camera triggers the flash immediately after the front curtain is fully open.
This means that, if my trigger mechanism induces a delay of more than 1.3ms, the rear curtain will have started moving before one or more of the strobes has fired. Although most radio and optical systems don't induce this kind of lag, if you use (as I did) a radio trigger on a master strobe and then optical slaves on the rest, the lag is compounded, and I occasionally found I was getting the black bars at 1/200 shutter speed. The weird thing is that it is not consistent and I have no explanation for that. I can fix the problem by using all radio triggers or dropping the shutter speed down to 1/160 or slower.
By the way, the significance of me mentioning the flash duration for my strobes is that, when using the shutter speeds close to your sync speed and if your strobe has a long duration - some have up to 1/500s or more - it is almost certain that the rear curtain will start closing before the strobe has finished firing. Instinctively, I would expect this to cause somewhat graded exposure across the image. My strobes have a fairly fast flash duration and I haven't noticed this effect but has anyone run across this?
What's better? That depends on a few factors... However, when considering the pros and cons, you have to look at a few different things. A couple that I found really relevant in this was:
TTL support. The major brands offer this through optical control, in your camera, but that does mean your camera either uses the built in flash or a mounted speedlight to do that. Radio triggers offering this are much more expensive than the ones without, but gain by not requiring line of sight. That's the trade there, though you mentioned line of sight (which I think is actually unreasonable in a lot of shooting scenarios) not being an issue.
Separated control. I do some macro stuff, notably water drops, and my technique uses off camera flash and long exposures in a dark room. If the optical option is used, the flash fires when the shutter opens, but if I go radio, I can use the commander off the camera with the test button. Subtle, true, but actually quite powerful for the right application.
Anyways, these were the "biggies" for me and in the end, I found the radio option to be much more flexible in my usage than optical despite the fact that I couldn't get TTL support for Pentax. Individual mileage, however, may vary. :)
The speed of optical versus radio has much more to do with delays and latencies in camera and flash electronic systems, than the type of waves traveling between the systems.
EM waves are so fast as to have no effect at typical photography exposure times. To know the speed differences of any system you have to know the electronic specs of each, radio or optical. I doubt the details of such are published by most manufacturers, but they would know best if you can get them to divulge.
An optical trigger reacts to the transition from normal lighting to flash lighting. Short of any additional circuitry (like pre-flash avoidance) we are talking about something like 10000 Watts appearing within dozens of microseconds due to a large gas discharge triggered by a strong ionizing pulse. There is nothing overly remarkable coming afterwards, and the speed of light travel does not really add anything significant to the equation.
A radio trigger does not work with anything near that power. Instead it uses a modulated signal at a speed and modulation frequency the detecting circuitry (often microprocessors) can reliably recognize and deal with. The signal-to-noise ratio is way way worse than the rather unsubtle action of an optical flash and it needs to be reliably detected even when disturbed by the electromagnetic interference of an actually firing flash at the same time. So the time frames the detection and decoding circuitry are working with are way longer in order to make a reliable determination.
For speed, simple optical slaves should be hard to beat.
Also, one needs to be aware that radio slaves not meeting the definition of "good" in other answers (eg simple 16 Channel 433MHz ISM devices) can be "slower" than expected, sometimes to the point of requiring you to go one or two shutter speeds below the camera's specified sync speed in order not to get partially exposed frames. This behaviour can be nondeterministic (one trigger even will be delayed several ms, another won't be delayed as much).
Likely, these receivers do not use a proper protocol with error correction but simply use statistical/lowpass filters (if there is enough radio energy with a recognizable modulation pounding on it in a given timeframe, they trigger - if there is interference, it will take longer; if there is bad reception, it will take longer). Be aware that ISM devices do not have any exclusivity on a radio band, a lot of other things (HAM radio, Microwave ovens when using 9xx MHz bands, WiFI on some bands) can interfere with communications at any time and require retrying the transmission, delaying it in the process. If the receivers were too liberal about accepting dodgy/interference-riddled looking trigger signals, that also would leave a bad quality impression - you would frequently have them triggering on interference itself, in the worst case setting off a strong studio flash right into a bystanders face (startling annoyance at best, an injury hazard at worst!).
I would not put it beyond the cheapest devices to use superregenerative receiver circuitry (itself an interference source!) or sloppily calibrated TRF circuitry (which can very easily degrade into a half-functional state).