I have a 14mm/1:2.5 prime that I got with my GF-1. Does it make sense to invest into a 20mm/1:1.7 lens? I don’t care much about the difference in focal length. I’d like to know if the speed difference is obvious, if I could shoot with lower ISO, under much worse lighting, etc.
It depends on what you're shooting.
if you're usually shooting towards to the end of your ISO range (for ex. at ISO 800 or higher in the case of your camera) then 1 stop extra will give you the difference between 800 and 1600 which is quite significant for your camera. The noise difference between the ISO stops is getting "bigger" (more noticeable) while the ISO increases so you will want to avoid that.
if you're usually shooting moving subjects you usually want to freeze them or to have them blurred just a little. For humans, this usually means that you must have 1/40 - 1/80 shutter speeds (very approximate values, don't flame me on this). In order to have such speeds in low/dim light you need a fast lens. See what shutter speeds your camera is able to obtain on a reasonable/usable (for your taste) ISO. It is that enough for you? If you have photos with a lot of noise because of iso and/or blurred subjects because of movement, then this is a sign that you need a faster lens.
if you're usually shooting handheld and your shoots are blurred because of handheld camera shake, this is another sign that you need a faster lens.
I don't know the lens, but usually the wide-open aperture is the "desperate" aperture. There are very very very few lenses which are at their best straight from their wide-open aperture. The wide-open is used usually when you are desperated to get the shoot. Usually stopping down will enhance the things considerably. Hence, having a f/1.7 lens stopped down at f/2.2 will likely deliver better results (wrt quality) compared with a f/2.5 lens wide-open. But again, in order to be sure here, we need to see some lab tests MTF charts etc. But, again, the vast majority of lenses behaves as I said.
So, if you don't have enough light to take good shots with your present lenses, I think that's better to invest in a faster one. Also, there are enough exposure calculators in order to see, based to your actual EXIF data of your problematic shots, if the new lens will really help you (ie. it will lower significantly the ISO, raise enough the speed etc.)
To get the same depth of field (meaning the same amount of subject matter in focus), you'd actually have to stop down the 20mm lens to a smaller aperture than the 14mm lens, thus losing the main benefit of the faster lens in low light conditions. That's assuming you want to keep the same amount of subject in focus.
You also said you didn't really care about the difference in focal length, but it's worth noting that the 35mm equivalent is 28mm and 40mm respectively, which is a fair bit of gap in the angle of view. You're going to have to change your positioning a fair bit to get similar outcomes.
At any rate, you might find these photography calculators useful so that you can compare a little bit more apples to apples. :)
Now, if you were talking about two lenses with the same focal length, it's likely a no-brainer. The faster lenses in that case are usually higher quality and better built, so almost always a better choice if you can afford it. Something for future consideration as you start to acquire more lenses.