That’s right. I’ve seen arguments over which scheme is better, but the second game’s scheme is definitely more orthodox.

I also keep hearing ME1’s combat described as “clunky” and ME2’s as “smoother”. Without much experience with this type of game, I think I just don’t have the skills to feel the difference.

You're probably playing on a PC with mouse and keyboard. The Xbox 360 Mass Effect controls were not great, but that was the original release.