Like several others, I think I have to choose Triangle Strategy as my favorite. It's probably an accident, but to me it felt like the perfect level of difficulty throughout. It seemed like every single battle resulted in me starting with what I thought was a good plan, watching my plan get shot to pieces, panicking and trying to reorganize, and eventually regrouping sufficiently to claw my way to victory. It made almost every single battle feel like an accomplishment.
I've said before that Fire Emblem is the comfort food of the genre, and Fire Emblem: Path of Radiance is the most comforting. Of all the FE games I've played, it feels like the most complete package. A great cast of characters, some really fun maps, no gimmicks that detract from the experience, and a lot of variety in approaches given the relatively large army size you can bring to each battle.
I know it's a heresy to some people, but I did not care for the story in Final Fantasy Tactics at all. That said, the battle system is fantastic. I love the heavy emphasis on elevation and area of effect attacks, which means you need to care about positioning a lot more than in many other games of the genre. And, of course, the job system automatically makes everything better.
And if people are going to use this thread for recommendations, I'll toss in the most obscure one that I really liked: Banner of the Maid. It's a Chinese developed alternate reality French Revolution/Napoleonic Wars era Fire Emblem clone with cute magical anime girls. And as ridiculous as that sounds, it works. The maps are fun, the challenge is there, and as cheesy as the concept is it takes itself seriously enough. It also has one of the best examples of story-gameplay integration I've seen. You know the trope in which the battle is tough, the heroes see no hope of winning, people are falling into despair, and the hero gives a speech and rallies the troops and uses that to somehow steal victory from the jaws of defeat? Well, one of the maps was absolutely perfect for that.