A very divisive topic in some circles lol. The main decision is probably between the PSP version (LuCT) and Reborn, though the PSP version also has an overhaul mod called One Vision that I know some people swear by, even if I've never played it myself.Which Tactics Ogre version tho? Because there are 3, all with gameplay and content differences.
I'd always recommend Reborn myself; the QoL it adds is just too huge for me to go back to LuCT, even if there some Reborn mechanics I'm pretty lukewarm on; the card buff system, mostly. Crafting in LuCT for example, was pure tediousness; it has a fixed failure rate, and you can't attempt to create items in batches meaning you have to make them one by one, even for base ingredients. And some recipes require quite a lot of ingredients, which all add up to just be pure awful.
LuCT also had a weird levelling system where it was classes that levelled rather than characters, which seems interesting until you get access to a cool unique class in the late game and realise you would have to grind it 30 levels to actually use it. Reborn goes back to individual characters having levels instead, which I much prefer. I also prefer the class balance of Reborn; in LuCT there wasn't much of that, the optimal party for most of the game would be to run a squad of just Archers and Ninjas, they were so much better than the other classes. Reborn did a lot to make some stinker classes actually pretty good; the standout for me being the Terror Knight. In LuCT it was really bad, by virtue of having one of the lowest turn orders in the game with only mediocre dark magic and debuffs to make up for it, while in Reborn they really excel as can openers for tough enemies; they can absolutely destroy an enemies attack and defence, turning what would be a very difficult encounter into something much more manageable.
On the other hand, Reborn limits the amounts of active abilities a unit could have from 10 in LuCT to 4. It's not qite so bad as it sounds cause stuff like Jump and Move+2 being changed to innately part if gear instead of taking up an ability slot, but I understand why some would see it as a step down in build variety.
Of course these are only a few of the differences and you may have already noticed I'm a bit biased, so it's always best to check these things out yourself if you want to decide between them! Its a great game either way, and something I'd strongly recommend to anyone interested n tactics games.