If anyone cares about my opinion:
SOR 1: Ugly graphics. Great, fantastic, amazing classic videogame music. I think this one may be the most fun all around, and I'm not tired of it yet.
SOR 2: Good graphics, feels the most sluggish of the series. Many consider this one the best of the three. Also has an exceptional soundtrack but not of the same classic quality as the first, in my opinion. In all a really good beat 'em up. Added the enemy life bars, which is kinda helpful, sort of. Got rid of the "A button calls the police" feature and replaced it with a desperation move like thing that drains the lifebar when used (real original, huh?). I still like this one the least of the three but it is still very close
SOR 3: The fastest, "loosest" feeling game of the series and probably also the best looking. Very different music, not like Yuzo Koshiro's standard "big city dance" style at all, more dark techno edge. You'll love that or hate it. I think this game is fun, but it takes a while to get used to the feel. Also added special move gauge that fills up and allows you to do a "rescue move" without draining the life gauge.
Now that I think about it, I love them all pretty much equally... sorry for wasting your time.