I might be wrong on this, but I vividly remember finding a quote from the Complete Encyclopedia months ago that described Palpatine as having found an apprentice [Anakin] who had "far more power in the Force" than his now-dead apprentice [Dooku]. I'm looking but can't find anything so far. So, don't take my word for it until I find it.
__________________ “The galaxy must experience the pain of death and the rapture of rebirth as I have. I will bring chaos. It is time for war.”
Well it's hard to say, because on one hand we're told he became more powerful when he embraced the dark side, whilst no one official has specifically said his mind set hindered him.
The closest we have is Filoni talking about how every fight plays out differently depending on the combatants mind set and context of the fights.
But even if it did hinder him, embracing the dark side enhanced him, so we need more proof of Anakin's superior Tk tbh.
Kenobi had TK contest with Anakin but he never had contest with Dooku, so strength of Dooku's and Anakin's TK can't be compared based on that. On the other hand Dooku is much more skilled than Anakin with TK, that's why he took out Kenobi without a contest. Anakin is more powerful and his TK is stronger than anyone's but he can't utilize it as skilfully and unpredictably as Dooku or Maul.
Anyway, during Kenobi's contest with Anakin, they got separated by Force explosion. If it did not happen, Anakin would eventually overpower Kenobi. It is a demonstration why lightsabers take precedence over Force fight, rather than prove that Kenobi's TK is equal to Anakin.
It's true we don't often see an actual force contest between opponents. It's usually just one catching the other off guard. And when we do see a Force contest (Luminara vs Ventress, Anakin vs Kenobi, Yoda vs Sidious) it tends to always have the same result, a 2-way Force explosion.
That being said Dooku gets in a lot of Tk hits in his fights, which almost always gives him a major advantage in combat. And when they do get hit by Dooku, Anakin has been shown to be capable of taking those Tk attacks much better than Kenobi could.