The "War of the Lions" port was released for PSP in 2007, and added two new character classes to the original game, along with new character cameos from Final Fantasy XII and Tactics A2, new animated cutscenes, and a story that actually made sense thanks to a revamped translation.
The iOS version keeps those changes in tact, but also promises less slow-down, auto-save when you receive a phone call, and Retina display support. Unfortunately, the game doesn't include the PSP's multiplayer option, and you'll need a 3GS or higher to run it.
Although the iOS version is lacking the PSP's multiplayer functionality, it's priced higher than the original game. The PSP game can be downloaded for $9.99 on the PlayStation Store. Plus, if you'd rather have a go at the old and largely incomprehensible translation, the original game is available as a PS1 Classic. (Also for $9.99, oddly.)
Check out a new video of the game in action, courtesy of Famitsu. It's important to note that this isn't a universal app; the iPad version will be coming sometime this fall, at least one month behind the iPhone version.