I've played both. I think the sequel (Wild Arms: Alter Code F) is better because it combined all the best aspects of the Wild Arms game.
The stories are about the same IIRC. There's the battle cancel system, which I think is the best aspect for any RPG game to this date. This may sound oxymoronic but as much as I love RPGs, I fucking hate time-wasting random battles. But I also hate it when some wild random monster is in the game and you gotta approach it, or the other way round, for a battle to be engaged. Which is why the battle cancel system in Wild Arms is Godlike for me.
There's a customization option too with some badges or whatever it was, which for me was quite tedious but is quite alright.
But the best thing about the remake is this IMO:
After all these years, I still can't get the melody out of my head
[youtube]Y8Fedfg8B50[/youtube]
Edit: So apparently, the original series have the exact same music. Didn't know that cos I never replayed the original ones but I did just replay the remake like 4 years ago.
[youtube]VVOFibwVMw0[/youtube]
Fuck I'm so gonna relive dem memories