Is it a role playing game with strategic elements or a strategy game with role playing elements? Yes, yes it is. Final Fantasy Tactics brought the sub-genre of tactical role playing games to the masses on the PlayStation in 1998. It wasn't the first but it was definitely the most successful and well known example to that point. It was a great game for Final Fantasy fans and strategy fans alike.
While the title makes it sound like more of a strategy game, the role-playing elements are much more than just superficial. This is really a true Final Fantasy style RPG, just with lots of of combat and much more detailed control over the combat than your typical Final Fantasy game. Final Fantasy Tactics is an excellent game and is really one of those must have games for the PlayStation.
Unlike other Final Fantasy games up to that point, battles occurred on a 3D isometric battlefield. Battles are turn-based and things like range, damage, and speed are all determined by individual unit stats as you would expect. Units gain experience, level up and increase their abilities as they participate in battles.
Final Fantasy Tactics has been re-released a few times over the years. It was re-released as part of the Sony Greatest Hits line four years after its original release. An updated PlayStation Portable version titled Final Fantasy Tactics: The War of The Lions was released in 2007. There was also a Final Fantasy Tactics Advance for the Game Boy Advance in 2003. It had essentially the same game play, graphics and locations but the story was somewhat different and it was a bit shorter though it had more side missions. A sequel to the GBA version titled Final Fantasy Tactics A2: Grimoire of the Rift was released in 2008. If you prefer to play the original on a modern system, Final Fantasy Tactics was released via the PlayStation Network for the PS3 , PSM and PS Vita in 2009 and I believe it is still available.
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After finishing it then try it with rom-hacks. You'll be in strategy RPG heaven again.
I never really got into Final Fantasy but its cool to see the old screenshots! Brings back some nostalgia.