I think he's perfectly fine when given the chance. No one could have sold that Anakin/Padme nonsense.
Contrast with Revenge of the Sith, he has a lot of good scenes...that aren't with Padme. The opera scene, from a performance perspective, is one of the best of the entire franchise, and the scene where Anakin and Obi-Wan say goodbye to each other really sells the tragedy of what the audience knows is about to happen.
I think a lot of that is due to Tom Stoppard having been the one who actually wrote the script, and I think Lucas also had Carrie take a pass at it. It's just better material.