A Vulcan stranger arrives a few seconds too late to save Nero's wife's life. So Nero destroys the USS Kelvin for not knowing where Future Spock is (???), waits 25 years (????), chucks Spock on an ice planet, blows up Vulcan, and then plots to blow up Earth (???????).
WHAT. I DON'T EVEN.
It wasn't just Nero's wife, he lost his whole planet, his whole culture, basically everything but his ship--at least from his POV. Did ya' pay attention to the movie? Cause the motivation for Nero is pretty clear: He's out to 1) Hurt Spock. Not just punish him, but hurt him. 2) Punish Vulcan and the Federation and in doing so (in his mind) save Romulus. He fired on Kelvin before he knew he was in the past--basically just coming out of the blackhole and fired on the first Federation ship he saw, and when he found out that he was in the past he raged and just destroyed the first thing in sight.
He was out for 1/2 revenge and 1/2, in his screwed up way of thinking, doing the right thing. He was motivated by loss, pain, grief, and anger.
Shinzon just came off as a spoiled child that needed a good ass kicking.
Rage can make one act in a irrational and rash manner. But after 25 years he should've calmed down.
Nero's actions only make sense if he was batshit crazy. Which is quite possible. His crew, or at least his first officer would have to be insane as well. Also possible, though less likely.
Thing is, crazy villains tend to be uninteresting, at least for me. But then, we have the Joker in TDK. I guess it's all a matter of presentation.