As I did not have access to the PSP version, I can't really compare to that, so my comments will be related to the PS1 version.

In a nutshell, I'd say I found the game to be quite a bit easier than my first playthroughs of the original, but a lot more annoying. And that's considering in my very first playthrough, an enemy stole Aloser's revivify, so I went the whole game without.

Pros:
- The voice acting is quite good, though very wordy and I was often skipping dialog once I'd read it later on.
- The new classes (compared to PS1) were fun, though I found the more free use of heals for example trivialized some early encounters, i.e. too many characters could heal in a pinch.
- I played through the C route and the first CODA so far and I appreciate the new story additions.
- The soundtrack is phenomenal, but it was that already, just improved in quality.
- For those unfamiliar with the original, the depth of class, gear and squad customization are sure to be a big plus, but it was mostly what I expected as a player of the old one.

Cons:
- The buff cards. A thousand times the buff cards. Atrocious. They clutter the game screen, bosses are unfairly buffed later in the game by just coming with a full set of cards, and get some 2/3 cards on the right character and a whole battle becomes trivialized anyways.
- Archers. What have you done to archers? Yes, I understand archers were very powerful in the original, but this goes too far in the other direction. The simple existence of equipment restrictions already makes it so you can't plop a bow on everyone so why nerf arrows so hard?
- Level sync/cap. For using the wheel of time and doing the other timelines, I understand level syncing, but the constant level caps per chapter and the syncs toward the end of the game are just frustrating. A solid tactic in most RPGs has always been to go and overlevel if you're facing some difficulties and this just prevents that. It doesn't even prevent you from becoming overpowered anyways since you can farm permanent buffs easily later on, just takes a different kind of grinding than grinding for levels.
- The chance of hitting attacks going for a more RNG feel with the activation of passives is kind of annoying and reduces the value of stats. No more AGI/DEX Haborym parrying everything but magic.
- The fact that there are multiple levels of spells instead of simply scaling off your stats means you don't really feel like your character is becoming more powerful, you're simply buying better gear. The AoE range being dependent on the equipped spell level rather than your stats, or (what I hoped for) something you can choose before you cast also restricts your options.
- Tankiness. Battles take far too long because of the availability of heals and generally bigger HP pools, even sped up, and the buff cards don't help. No one likes bullet sponges.

Conclusion: The game is still fantastic. For anyone who hasn't played the original, I can easily recommend getting this for the fantastic story. The graphics are much nicer, and the spells look alright, though I prefer the pixel style of before rather than the current particles based effects.
For those who have played the original (and maybe the PSP version) this is a much harder sell. This is basically not the same game, the gameplay changes are too big and, in my opinion, few of them are for the better.
If you're new to Tactics Ogre, buy the game. If you aren't, buy it on (a deep) sale.

Can't decide if I like it or not.
I started playing it but it has a really slow start and I lost interest. The plot is cool, if somewhat generic, but I'm sure it's one of those things that makes more sense 40 hours in and I didn't get that far.

Combat was alright, but the animations are a little janky and as far as I got with the sidequests and such, it feels like MMO fetch quests in a single player game.