It's really tough for me, this are undoubtedly my 3 favorite Final Fantasy's and on any given day I could prefer one over another. When I first beat IX I thought that it had topped FFVII. However, years later, re-playing both many times, I had to switch my opinion:
The battle flow in FFVII greatly surpasses not only FFVIII and especially IX. In VI, VIII, and IX, you spend a great deal of time sitting there watching the battle unfolding, waiting for lengthy animations to end so you can input your next characters command, sometimes finishing long before the next lengthy animation will end. These 3 games each took the "A" out of ATB. In VII I felt the flow was perfect, a bar fills up, you go, you see what happens next, you're always on your toes. It also scores points for having the "Recommended" battle speed option, something no other FF has had, only stopping battle for lengthier animations such as summons. The camera angles and movements were also much more dramatic, whereas the camera was pretty static in VIII and slightly behind in IX.
We can argue all day about story, characters, and plot devices, but we couldn't come to definitive conclusions. However, battle is an important part of RPGs to me, and VII dwarfs the others, not only for the above reasons, but also because VIII started, and IX followed, the new FF tradition of having only 2-3 monsters on screen, and very rarely any more than that.
I also have to say that it's unreasonable for all of you to jump on Super Sepiroth for saying that it's child-like. FFIX is undoubtedly the corniest game in the series (again, it's one of, and on some days, my favorite). Zidane is a warm and fuzzy main character accompanied by warm and fuzzy sidekicks, the only time his personality changes is in pandemonium, which was actually pretty unbelievable because he unexplainably buys into Garland's logic after being so defiant against it. He's almost the definition of 2 dimensional. Also, VII and VIII in many cases "show" you the themes they're trying to convey, whereas IX has to "tell" you, such as Garland's lengthy monologue on societies. In visual storytelling, this is a very poor technique, and a huge mistake.
Lastly, I just want to say, that the amount of effort that IX put into making it seem like a "true-to-FF" game is a very un-FF thing to do. Having played all the FF's, the references don't really enrich the game for me, because in VII and VIII they were all more subtle and were more rewarding that way.