I've only played Revelation and Birthright, but overall Birthright was best. Here are the important things for me when it came to choosing:
Characters. Birthright. They weren't all very compelling but all my favorites, Ryoma, Saizo, and Takumi are from Hoshido. Also I'm absolutely terrified of Camilla.
Story: All. Birthright was a cliche but I'm okay with it. Conquest seems interesting but it means I have to join the side I don't like. Revelation was hollow but explained why Garon was evil rather than, he's evil so the story has a villain.
Gameplay: Birthright. I actually liked the simplicity of Birthright. I didn't have to mess around difficult objectives, I could just focus on eliminating my opponents one by one. Which is more my style anyway.
Weapons: Conquest. I haven't played but I've seen the dusk armory's gear through Revelation. I like longswords over katanas and also giving Blazing Yato a D-guard was a mistake. It looked like a cutlass not a katana.
Common Sense: Birthright. If Garon is evil you don't join his side, you fight against him. Also who sides with the people who lied to you your whole life, locked you in a tower, killed your father, and killed your mother with no regard for the fact you might be killed too.
Ability to Level Grind: Birthright. You can't grind in Conquest.
Music: Birthright. I just like it best, but I love the song Lost in Thoughts All Alone and I really like how each path has different lyrics for it. So each path gets credit for great music.
Awesome Final Battle: Revelation. Overall it is a hollow game but give the final battle credit. You fight an enormous dragon, in space, with awesome background music, using a MAGICAL, FLAMING, CHAINSAW SWORD.
A Happy Ending: Revelation. Normally this isn't a requirement but I recently finished multiple television shows and video games with sad and depressing endings. Revelation is the only path where a: you don't have to kill any of your siblings (adopted or true) and b: my avatar's wife survives. Only two characters died and it's unfortunate but I can live with that.