I suppose, reading the last comment, that people usually side with their first ever game, that might actually be half the reason why I chose Spirit Tracks. The game has a level of nostalgia for me, as it was my first ever Zelda game.
In Spirit Tracks, I really did like the story alot, because not only do you want to save the kind person that you just met that happens to be a princess, you also have the fate of the entire world on your shoulders from the beginning of the game, wheras in Phantom Hourglass you origionally start just to save your best friend that ALSO happens to be a princess. It's like that in many games, such as in the Wind Waker you start the quest to save Aryll, and in Twilight Princess you start to save the Ordon kids and Ilia. Also, in Spirit Tracks, you are presented with the main enemy quite early. This disappointed me in PH, because you get the spirits, then get Tetra, then have to continue your wild goose chase and then finally you are presented with the main enemy. Although, I suppose this storyline could have been used to make the game longer, it wasn't what pleased me most.
A major point in the argument would be the center dungeon of each game, the Tower of Spirits, or the Temple of the Ocean King. Almost NO ONE liked the TotOK, me included. It was WAAAY too repetitive, and the time limit and inability to kill phantom's just p'd me off. In the ToS, you not only had no time limit and the ability to kill [possess] phantoms, but the Phantoms had different qualities, you could possess them, and YOU DIDN'T HAVE TO REPEAT EVERY STEP OF THE WAY!
The companion of the game also made a big difference to me. Zelda hasn't accompanied Link on any adventure before Spirit Tracks, which gave it a totally new feel to it. Ciela was basically a copy of Navi, but aquiring a whole bunch of annoying fairy buddies. I think here, Nintendo just ran out of ideas.
To me, Phantom Hourglass was just a re-make of Wind Waker, but with different characters. The quest starter, either Aryll or Tetra, is taken away, you chase, then have to go through a couple of dungeons, then you find the quest starter but somethings wrong, either you can't take her or she's turned into a rock. Then you have to do a couple more things, go through more dungeons and chase around after things, then you can go and defeat the final boss.
The difference in controls between the two titles isn't very different, as many things were the same, but the things that were different were major. In Spirit Tracks the roll controlling was much easier, as I'm sure everyone can agree. The train was slow, and the boat got you around faster, not to mention the ability to warp from anywhere in the Great Sea. The item selection control was better in Spirit Tracks, especially when in battle, the ability to stop everything and get what you need was much better.
The graphics and music in Spirit tracks were also much better than Phantom Hourglass, in the later game the graphics became more refined and smooth, wheras in Phantom hourglass everything wasn't as nice, to me, it was as if they were achieving a handheld, cel-shaded Ocarina of Time. The music was also much better in Spirit tracks, including the dungeon music. It got extremely annoying in Phantom Hourglass, to be repeated every time you went underground or in a dungeon. This was improved in Spirit Tracks, as the final dungeon's music changed from the earlier ones. I loved the Tower of Spirit's music, and especially loved the Sacred Duet. I mean, who couldn't? The Lokomo's songs were also very well done, the village music was different, but similar at the same time, the haunted realm music was incredible, the final boss battle's music was amazing, and yeah, I think I'm just starting to rant now. I'm not saying that Phantom Hourglass' music wasn't good, in fact I quite liked Oshus' theme, but the audio from Spirit Tracks just stood out for me.
I havn't quite finished Phantom Hourglass yet, because I want to 100% the game and I still can't quite catch a Neptuna, but from what I have seen of the boss battle, it doesn't look as fabulous as the three-part one of Spirit Tracks, not to mention the bonus little song in there.
I just have to point out here, that I really liked the little easter egg type things that were in Spirit Tracks from Phantom Hourglass. An obvious one would be Tetra's appearance on the stained-glass window above Zelda's throne and the mention of Tetra from Zelda when she merges back into her body, "Tetra! Please give me your blessing!" Another obvious one would be Linebeck III, and Alfonzo's similarities to Gonzo. Makes you wonder, they're probably related, aren't they?
Don't get me wrong, I really enjoyed playing Phantom Hourglass, I thought it was definetly up to Zelda standards, but I have to say I prefer Spirit Tracks.