The very fact that he spends so much time and effort obsessing about how Picard sees him is for me the selling point on the theory that he goes after Earth in order to impress. More specifically, he does it in order to impress Picard.
Don't quite agree. I thought Shinzon went after Earth because he finally bowed to the pressure of his Romulan allies-of-convenience, who wanted him to do this the whole time. I don't believe he had any interest at all in attacking Earth, much less using that action to prove something to Picard. By that point in the movie, I think both men realized they were not the same as the other.