No, I don't think FFX-2 was rushed, and it didn't have low-budget due to FF: TSW. After the huge losses of FF: TSW, Square got their losses sorted out when Sony bought $120,000,000 worth of Square's stocks, and FFX sold millions of units, which certainly made up for the movie's losses.

I think FFX, KH and FFX-2 all rely less on FMVs, but that's because they can use the game engine to show more things than before. With FF7-9, the in-game graphics just weren't enough to show some things, for example accurate facial expressions, but now it's totally possible. However, when there is an FMV, that is very high-quality. Personally, I've yet to see an FMV that is better than the 1000 Words scene, which I consider a masterpiece cinematic, and it's also innovative in a way that practically no game has ever done something like that, although FFVI with the opera scene was quite similar.

While there isn't too much main story, there's loads of character development and sub-stories. If you take your time to explore all the optional quests, the game is extremely emotional and also deep. The style is just different since Square Enix wanted to give the players some freedom with their paths after the linear FFX. Technically the graphics and sounds are very well done, surpassing even those of FFX's, so it isn't rushed that way either.

Some people call the ending rushed. However, I don't think so. The final battle gave some nice tribute to FFX's, and it also did a good job with showing how Yuna has developed during the two games and how she doesn't want to repeat the past mistakes. It was a well done final battle and climax, and the endings after that, although short, were well done and certainly not low on the emotional side.

Now that I played FFX for the second time, many conversations and scenes in FFX just wouldn't make sense if FFX-2 didn't happen, so it's likely that Square was planning a sequel even during the writing of FFX, so FFX-2 wasn't just a sudden decision to get some extra cash. I have a feeling Square had a huge story planned, but they couldn't fit all of it in FFX, so they had to put the rest to FFX-2. This makes sense since (SPOILER)you can't just kill the main character in the middle of the game and have Yuna become the new main character for the rest of the game and then have the main character return, which would be the case if FFX and FFX-2 were just one big game.

Overall, I don't think FFX-2 is rushed at all. I even think it's better than the first part. I didn't like FFX during my first game, but I liked FFX-2 a lot, and then playing FFX for the second time after playing FFX-2 also made FFX make more sense and feel deeper.