Though it's a bit hard for me to choose seeing as how there's plenty of good ones, I would have to go with the Super Nintendo as my favorite console and the Gameboy Advance as the best handheld. The reason for this is because they both had amazing graphics and music for their time (and still do in my opinion), as well as a very large selection of great games (especially true for the SNES). Overall, these two are almost tied in terms of functionality and gameplay, but I still have to say that I would choose the SNES over the GBA as the greatest gaming system of all time. This is also in part because of the larger RPG selection of the SNES console.
So, to sum things up:
Favorite console: Super Nintendo Entertainment System (SNES).
Favorite handheld: Gameboy Advance (GBA).
So, which are your favorite gaming consoles and/or handheld devices and why?