Hi Jiftyj, since I own both games, I have to say that I really like the story of PMD Sky better than PMD Gates to Infinity. Sure, PMD Gates to Infinity is a very nice and well-made game with the graphics and sounds, it has everything but.. the story is indeed a bit on the short hand. Although PMD Gates to Infinity had a nice feature of making your own paradise with your partner, there isn't that much left to do in post-game. You can battle a very select group of legendary-boss Pokemon in post-game and obtaining them in your team is impossible unfortunately.. Also the battles (especially with bosses) are a lot easier (I remember thinking while battling as a Pikachu: Whut? Defeated Kyurem with barely any scratches at all O_o?!). A good thing what I also liked was that in PMD Gates to Infinity wild Pokemon suddenly could evolve in battle, but a downside of this feature is that when you are training to level up, a wild evolved Pokemon whipes you and your partner out within seconds O_o waaaayy to over powered, especially when you just started your game.
Like in PMD Sky and the previous series, there are a lot more Pokemon you can choose from and obtain. The story is a lot longer too and also has a large post-game in my opinion. I remember playing PMD Sky the most because of this :3 And I liked the fact that PMD Sky seems a bit "harder" to play than PMD Gates to Infinity.
So, if you prefer a very nice looking, somewhat simple gameplay, but fun game for a short period to kill time, PMD Gates to Infinity is your game. If you are looking for more challenge, longer and harder gameplay and still want to feel the thrill of obtaining almost every Pokemon, when "finally a specific Pokemon wants to join your team", I would say you should choose PMD Sky