If you are buying the PC version, absolutely. If fixes the technical flaws in the 360 games. It also adds a few cool new features such as the Turbo feature for upping the speed of the battles.
If you are buying the 360 version, I'd rent it first. The technical flaws maybe a turn off for you. If you install the game to your hard drive it reduces but does not eliminate them. I got pretty far in the 360 game before I picked up the PC version.
If you doubt my affinity for the game you can look up my steam account, which is also Darc Requiem, my best friend was laughing at me because for the first month I had steam. I had a rating of 10 purely from playing The Last Remnant. I could technically finish up my third play through but I want to clear the Ancient Ruins.
The battle system is the real deal breaker on the game. I absolutely loved the battle system in TLR. Especially later on when you can have multiple unions, up to five, under your control. The battle system is almost like a turn based/strategy RPG hybrid. It's hard to describe and its best to experience it yourself.
The music in the game is outstanding. Some of the best I've heard in a JRPG in sometime.