He is an entirely two dimensional villain. Khan was awesome due to his history with Kirk, his plain motivations and his ego. Shinzon is just a cardboard cut-out. He seems to not really have any singular motivation.
I think he has a motivation, but it's nothing stated in the movie or as easy to access as Khan. The genius of Khan is while he has very clear-cut motives, he fits into the motif of the movie. Genesis, as well as Khan, are creations of our genius that out-paced our morality. Khan works on many levels, is my point.
Shinzon's motivation is to find fulfillment; his place in the universe. He is a very confused, young man. He doesn't know if he wants to destroy Earth, or if he wants to learn more about being human from Picard. Where is his place in the world?
"The Remans have given me a future, but you can tell me about my past. Were we Picards always warriors?"
"I like to think of myself as an explorer."
"Were we always explorers?"
He builds a connection with Picard, here. He sees himself in Picard, and vice versa. This allows him to consider life in peace, being human.
"Do not forget our mission, Shinzon. We must act--now!"
"We will return to the Scimitar. I was merely curious about him."
Reality comes back to him. He feels trapped by his mission, his Viceroy, or pseudo father, beckoning him to return to his warrior ways.
His relationship with Picard leads to this exchange:
"It's about destiny, Picard! It's about a Reman outcast--"
"You're not Reman!"
"And I'm not quite Human! So what am I?!?"
Why would he explain himself otherwise, to his enemy?
Picard recognizes that he can have an effect on the man Shinzon becomes! He realizes that he is looking for fulfillment. And, therefore, Picard says this:
"Oh, yes. I know you. There was a time you looked to the stars and dreamed of what was out there."
"Childish dreams, Captain. Lost in the dilithium mines of Remus! I am what you see, now."
Shinzon is trying to convince himself as much as he's telling Picard. It makes little sense for him to continue talking to him, to let this questioning and lecture go on. But he does it, because he is conflicted.
"I see more than that. I see what you could be. The man who is Jean-Luc Picard and Shinzon of Remus could never exterminate the population of an entire planet. He's better than that."
Conflicted, he says it with more authority now. He knows Picard is right; he's getting to him. But he has to stay with his Reman brothers.
"I can't fight what I am!"
"Yes, you can!"
And here is where he makes his choice. This is where the movie turns and Picard loses all hope that he can win this one over.
"I will always and forever be Shinzon of REMUS! And my voice shall echo throughout time long after yours has faded to a dim memory!!"
When he says
"Kill everything on that ship," he is recognizing, just as Khan did, that he is defeated. Picard will never surrender. His boarding party didn't bring him Picard. And Picard is bound and determined to stop him. He must stop the Enterprise to continue on his mission, whether he survives to rule the Romulan Empire or not.
I think it's very clear to anyone who's asked that question of him or her self: What am I? Where do I belong? Where will I find fulfillment? What are these urges within me?
He's not as committed as Khan, for sure. He's a young and troubled man. He doesn't feel at home with Remans or with Humans. That's a terrible place to be. He has gotten what he wants--freedom. Now, what does he do with it? All that talent for warfare and the ability to move an audience of Remans to revolt and he cannot deal with his personal demons.