I used GnuBoy long ago, and while it had some okay features, it also suffers from screen tearing among other things, and I think it has ben abandoned for years, so I can't recommend. I also tried to use Rin Wii, but I find it's also quite outdated by today standards (last version is from 2008).
That let's us with VBA GX, which does a good job for GB/C games, and Retroarch's GAMBATTE Core, which also works nicely.
I guess the pros of VBA GX is having a nice visual GUI, and is for the most part easy use. Has some video options, but original GB games are your usual 4 shades of green. You theorically can use custom palettes, but I never tried to do it as you need to input the color numbers one by one (at least on the custom palette menu). Also, I personally find the GUI, as pretty as it is, kinda clunky for my taste. I would recommend for people who just want to play gb/c without too much tinkering, as, as far as I know, the emulation is fine.
The downsides of the GAMBATTE are married to Retroarch itself, as you need a bit of tinkering and navigating around simple menus to configure it initially, mostly setting the correct GB aspect ratio. But once that is done, I think it's the superior emulator. Games work great, I find that once you have the aspect ratio down, Gambatte offers a better picture, and also has "Core Options" which let you change the palettes of the game you're playing on-the-fly, without even needing to reset the game. Also, while the interface of Retroarch is really simplistic, it's also more agile to navigate around. I would recommend Gambatte (and Retroarch) to those who are not afraid of tinkering in order to get the better experience (at least, in general).
I always have both on the SD for my Wii, but I tend to use Retroarch's 1.0.0.2 Gambatte core most of the time. Other people would argue that the pretty menu on VBA GX would make it a better "app", but I care about emulation, personally, and i find that Gambatte has the edge in that regard.
Now, maybe in the future, when mGBA improves its GB/C emulation, will take the lead against these two, as picture quality seems to be superior than VBA GX (again, just my opinion based on what I've tried), but also seems to be more simple to use than Gambatte/Retroarch. Kinda the best thing of both worlds.
Not to mention that mGBA is THE best GBA emulator on Wii bar none, so you would only need mGBA for all your "Game Boy Needs".