I own both.
Others have mentioned that AMH plays like a homebrew, and I agree although I don't think that's all bad. It has some really creative stuff, like the ramp with the jump spot it in, and although the sounds in it aren't sampled at the highest quality, the theme integrates the homebrew nature of the game with the sounds and everything else. It is definitely a funny game, which is difficult to get far in, but it has the ghost where you can go bash on it somewhat if you're not great. Overall, it's extremely solid and I don't expect it to go anywhere.
GB, first, I like the Premium much more than the Pro, and that is usually not the case for me with machines. In fact, GB is the only premium I have of any machine. Except the translite, the Pro translite is FAR the best one. I play GB the most of all of my machines right now, although that's partially because it's the newest game and I have been so buy I rarely have played it.
Having said that, GB does have some oddities I don't like. There are two video modes, but you always get to pick which one you want to play. One of them is completely random and basically worthless. The other is worth a TON of points (too much, I think) and has odd software quirks in it. It's called Don't Cross the Streams, but you CAN cross the streams in some cases, and sometimes the game automatically moves your zapper in the wrong direction when it shouldn't, meaning you can't win. Neither video mode is really "fair", and the fact that you can skip one always is just silly.
The gameplay on GB takes a while to figure out. You really need to be able to play it a lot to start developing strategies. Once you have, you can really play the game in different ways, which I do appreciate.
If I HAD to pick just one, I would probably get an AMH if I was buying because they are rarer and if you know where one is for a good price, you won't necessarily have that chance again. If I was told price didn't matter but it had to not leave my gameroom, it would be really close, but I think I would pick GB by a hair, just because the theme is one that I really love, and having a good game with a theme that I love seems really rare.
Both of them for me though are top ten games.