Shinzon was insane. Raised in a mine, subjected to constant abuse and taught to hate what he is. If you've had any experience with mentally ill people, you'll find their motivations don't always stand up to scrutiny.The sense I got from the movie and Shinzon (and this is just my feeling), is that he was planning on enslaving the Romulans after he used them to help him defeat Earth. So eventually the Remans would be the ultimate power on the planet(s) and in command, while the Romulans would be working for them. Poetic justice. Why kill them when he can make them slaves and make them feel what he felt.
Why not do that from the start and forget about destroying the Federation? There also no evidence he was planning that, so this just kinda guess work. That would have been nice to show, because him acting in Romulan Empire's interests didn't make sense.
Anyway you slice it, his motives for destroying the Federation were extremely vague and convoluted. He had motives for hating the Romulans, he even had motives for wanting Picard, but destroying the Federation, that made no sense.
IMO Shinzon wanting to wipe out Picard and humanity because they lived such privalaged lives while he suffered endlessly, and because he's a copy of a great man and would never fit in there, was believable. It didn't make rational sense, but it wasn't meant to.