The primary difference is in the films he isn't acting on his own will as much as listening to what his added arms tell him to do. It makes Ock a puppet, in a way. I suppose it could be argued he was
more insane than the film would like you to think and the arms aren't so much talking to him, but his insanity projects his own malevolent desires into something he can communicate with. But the film makes it pretty clear the arms are talking directly to him, a separate entity which shares his brain. That isn't a minor difference. Ock is a megalomaniac, and a egotist, he wants to succeed no matter the cost, and prove to the world his genius. All his decisions, all his own doing.
Now to be fair, this stuff only dawned on me recently, when I realized in altering Dr. Octopus, they essential shafted the Lizard. The sympathetic scientist is supposed to be Curt Connors, but that characterization was taken. It is why Connors in Amazing has that feeling of "been there, done that" to some. Which makes me wonder why they left out his family as that would have been the biggest thing to set Connors apart. I have seen people say Amazing shouldn't touch Dr. Octopus because the portrayal in SM2 can't be topped. For these reasons, I disagree.
If I recall correctly, the "good side" of the Sandman started to come around in the 80's, most likely because the character was wearing thin, so the idea that he is just a common crook isn't too far off the mark. I thought Sandman was interesting in 3, and didn't initially mind the shooting ret-con (because at the end of the day, the incident is still Peter's fault, and he wouldn't let go of that guilt regardless). I didn't even mind that Peter forgives him, but the way that it all plays out in the film is undeniably "