how bout this? Had Anakin attacked Palps, Papls might have used it as an opportunity to test Anakin himself, being that he is better than Dooku, and maybe, just maybe might underestimate Anakin himself, which Anakin could capitalize on. We dont know if Palps would have used the force in the duel. He could prefer lightsabers until he deemed force powers necessary. If so, Anakin could win, although not easily, otherwise, at THAT point in the movie, Sidious takes him, but not easily either.
Also as far as the Dooku/Anakin thing, this just kinda came to me. Dooku did have an advantage...it was more or less his ship which he knew the layout of (as stated), he KNEW he was going to fight the Jedi and had time to prepare, whereas Anakin didnt know he was going to be fighting Dooku. Also, if you want to take Dooku's word itself...he apparently reveres lighsaber skill as more pertinent than knowledge of the force, kinda like a tie breaker.
"It's obvious this contest can not be settled with our knowledge of the force, but with our skills with a lightsaber."
Or something close to that. Im sure if I messed up even one word, Rampant will be quick to correct me, but to me that means he holds lightsaber combat "in such high esteem".
Anyway, just wanted to add that to further PROVE that Anakin>Dooku... 😄