I'm in the process of completely recapping my first TG16 right now. But I've repaired a dozen or more flat panel monitors/TVs as well as 2 Sega Genesis's. There definitely is a difference in capacitor quality, but the quality also depends on the application. Monitors and TVs seem to stress capacitors far more than old school video game consoles. As such, capacitor failure is much higher in monitors and TVs. The brands I've heard great things about are Panasonic (the brand I always use), Nichicon, and United Chemi-con. Of course, within any given manufacture are multiple "series" and knowing the correct series to use makes a big difference as well.
For Panasonic, my preference is FM, then FC, then M, and lastly FR. FM and FC are very similar, FM has better specs and is typically cheaper, but not always available. The other series I'll only use if neither FM or FC are available. As a general rule to capacitors you want a low equivalent series resistance (ESR) value, which the FM and FC have. The job of a capacitor is to hold a small charge, and then release that charge when the voltage drops. How freely the capacitor releases this charge is the ESR value. As capacitors age and dry out, they tend to hold onto this charge and resist giving it up. Thus older (and crappy caps to begin with) will have a higher ESR value. ESR is the most accurate measure of how good or bad a capacitor is. Unfortunately, very few multimeters can measure ESR. You typically need a special ESR meter - I have the Blue ESR meter (
http://www.anatekcorp.com/blueesr.htm).
Bringing this discussion back to retro video games. As I recapped the TG16 I measured the ESR of the original caps as well as the new caps. The caps I took out all had higher ESR values, but none of them were so high that the capacitor would be considered "bad." In a week or two I'm going to post pictures of my recap job and I'll include ESR values before and after the recap.
One of the big exceptions to the rule about low ESR being the best is audio capacitor use. There's a whole special class of capacitors for audio use. I believe one of the most respected names is Elna. Obviously, video game consoles audio in them, so if recapping them do you need to account for that? Well a lot of people out there have tested general purpose caps in audio applications. Most people agree that the Panasonic FC and FM caps are the best general purpose caps for audio applications. So if you stick with Panasonic FC/FM then you should be good to go.