I have been using a Nissen Di866 mark II speedlight (heavily diffused) on my Nikon D800e, for macro photography. I now need to replace the Di866. What particular specifications should I look at when comparing flashes to indicate which would allow me to get more light on my subjects?
With hotshoe flashes, the spec you're going to be looking at is the guide number, which is the closest thing we have to give an indication of the light output of a flash. This is given as a distance, at a given ISO and zoom setting. In usage, the guide number, divided by the f-number of your aperture setting should give you the distance the light can travel from direct bare flash.
For example, a guide number of 60m at iso 100, zoomed to 200mm is very common for most full-sized speedlights. It's what your Di866 II sported in its specs, and it's pretty much what you'd get from every other full-sized speedlight on the market. But.
Why directly comparing guide numbers doesn't work
Guide numbers in specs are deceptive. Just getting a unit with the highest guide number may not actually be getting you anything more powerful than what you had. Different manufacturers report guide numbers in different ways.
When put into identical lighting setups, the Canon 600EX-RT (which had a GN of 60m) gave identical output at full power to the older 580EX (which had a GN of 58m). Because the older 580EX only zoomed to 105mm, and its GN was given at that zoom measurement. And there's no simple math to equate for different ISOs or zoom settings.
Nikon's SB-5000's guide number is given as 34.5m. But it's measured at iso 100, zoomed to 35mm. It's also been measured to be more or less the same output as those speedlights with a 60m (iso 100/200mm zoom) guide number.
The reason the zoom setting has such a huge effect on the measurement is because spread changes the distance the light can travel. The more tightly focused the beam is, the farther it can go. And if distance is how you're measuring the light, it can look more powerful.
But maybe you want the power to be used to spread the light for a larger subject. The modifier you use on a light, the zoom setting, whether it's in a reflector or not, whether you bounce the flash... this can all change how much light is actually falling on the subject when you measure it.
This is why the Godox V1 round-headed flash has a guide number of 28m, which makes it look drastically less powerful than a 60m GN traditional fresnel-headed speedlight. But its measured light output is, actually the same or slightly higher (0.1EV) than those 60m GN speedlights. The round head on the V1 is limited on zoom to 105mm, and it has a much wider and more even falloff and spread than a fresnel head. The whole point of a fresnel lens is to focus light and throw it farther.
Different types of light use different units
In addition to this, continuous LED lights have their output given in W ratings of the bulbs, or lumens, while studio strobes are simply rated with Ws/joules of energy consumed at a max. power burst. Different bulb efficiencies can make two strobes rated at the same level have different outputs.
In short, the easiest way to compare apples to apples is to find some obsessive testing geek on the interwebz who's actually put together a measuring setup and tested it with a light meter, like Petapixel did for a bunch of Godox lights.
My hot take
Speedlight-wise, you're not going to get much more power output than the Di866 II gave you. Any full-sized speedlight you purchase new is going to be equivalent, even the $1,000 Canon EL-1 and Profoto A10. If you want more power output, then you'll probably have to look at off-camera strobes, such as the Godox AD200, which would require a compatible radio transmitter to remote control the strobe, since there's no foot to put in your hotshoe.
However, whether this would benefit you as a macro shooter is hard to say, depending on what you shoot and how mobile you need your setup to be. Flash exposure is controlled by iso, aperture, power, and distance. And at close macro distances, most people don't need a whole lotta power to light something. And most macro shooters using flash are more into getting light from multiple directions, which is why ring flashes, twin flashes, and multiple small flashes clipped to a lens ring are specifically designed for and marketed to macro users.
You may simply need to increase your ISO if you're keeping it at the base setting. It is, after all, why we purchase cameras with bigger sensors these days. Or, you could open up the aperture and learn to do focus stacking.