This is hard a very hard choice. I really enjoyed both games so I will have to dig into this.
Firstly I did like the fact that you could explore the galaxies in the first game, although the second lacked that, you could get more varity in the galaxies of have less stars in each galaxy but more galaxies altogether.
Both games are not that hard although they do have the odd hard level. The first game had, Luigi's Purple Coins, Lava Spa Daredevil run and that horrible Sling Pod level. Galaxy 2 had A Scroll Down Rolling Lane, Stone Cylone and The Prefect Run. I remeber dying more in the first game than e second so the first may be harder but the second was far from hard but still not piss easy.
Galaxy 2 had much better Powerups than 1. Bee Mario was creative but it was just a flying powerup, Boo Mario was fun but underused, I liked Spring and Ice Mario however. Galaxy 2 has Bee, Boo and Spring return but introduces the Spin Drill which can be used to solve puzzles and the powerup is used quite nicely (if only it showed up more), Rock Mario was fun but needs to more used more. Could Mario was a very creative but is very overused. There is a massive problem with useage of Pwoerups in each game but even though the Powerups in that game were much better, it was more of problem in the second game only because of the fact the Cloud Flower appeared at least once in every world. While the other two new powerups only appeared in only one galaxy in the worlds they featured in. Galaxy 1 just had Powerups used way too less.
Galaxy 2 had Yoshi who appeared often enough (unlike NSMBW) and had a lot creative ideas, all three of Powerups are nice and not too underused. And it felt smooth playing as him as well he was a good addition.
Galaxy 1 had a much better hub world, Galaxy just had Starship Mario which had next to nothing to do there, Galaxy 1 had large easy to navigate hub world, with 6 domes which held most of the galaxies. Peach's Castle beats both of these hubs however.
Galaxy 2 has a much better co-op mode but than 1 but that's only because there's the co-star Luma.
Galaxy 1 had the better plot only because Peach's castle gets lifted.
What I don't get is why people say Galaxy 2 is a low quilaty expansion pack, it's not. It feels like a game that's taken an idea and expanded on it what all sequel's are supposed to be right. It had a lot of new idea's and concepts, the only dull one being the Green Stars. It wasn't unoriginal sure the first game is more original but all first games of series' are. It still felt fresh.
Both games have amazing soundtracks so I not going to dig deep there.
I liked both games equally and I will stay that way, both games have their ups and downs. And Galaxy 2 doesn't have much flaws if you dig deep.
I do NOT want to see a Galaxy 3 however.