There's more of an artsy and eerie feel to the first one, second one fits the blockbuster-guns-blazing-modern-special-effects-and-explosions type.
I think both were good at what they did. But my personal experience is this; First one I first watched when I was about 7,8 years old on tape, a few years after release I guess, and for some reason Arnold scared the $#@! out of me. So as a kid it was certainly an unpleasant experience. I didn't watch it again until maybe late 90's.
The second one I went to the movies when it came out as a teenager. I left the theater with my mind blown. It was simply the $#@! back then.
Interesting post. But if you have noticed, in the 1st part Kyle Reese [Michael Biehn, the actor] tells the police John Connor found the time machine and after Arnie's and Reese's pass to the year 1984 he destroyed it. So there's no good explanation in the 2nd part how the time machine appeared again.