In ROTS, Palpatine knew Anakin was a close equal to Dooku, but he also knew Dooku was more powerful than Anakin. Palpatine also knew that Anakin had the highest Force potential of all time and he wanted Anakin to be his successor in the rule of two not Dooku.
Palpatine knew that the only way for Anakin to defeat Dooku was by tapping into the dark side of the Force. If Anakin did this he would surpass Dooku and carry out the rule of two, also Dooku was much older than his master Palpatine and didn't have the potential to defeat him and become the Sith master but Anankin did.
Palpatine was the one giving Anankin Force visions of Padme’s death and he knew Anakin would do anything to save her including joining the Sith order. Palpatine was a master of deception and knew exactly what he was doing.
Just like Luke's situation he wasn't more powerful than Vader it’s just that Palpatine would do anything to get Vader replaced because Luke had potiental to be twice as powerful as Vader same with Anakin and Dooku Vader and Dooku were more powerful than their replacements it’s just that Palpatine gave the challengers a handicap against their oppenents AKA the dark side of the Force.
Both Vader and Dooku were victims of Palpatines foul play. If Vader and Dooku fought their replacements without their replacements having handicaps the favor of the two battles would fall into the Sith lords hands having them as the victors.