Registered: Feb 2015
Location: Heavens of Mystic
The Birth Place
By powers equalized you mean Sidious is brought down to Dookus power by this time, so by extension your asking who wins in a saber deul. No matter what if their equal then Dooku can hold his own in the force if powers are equalized. However in a saber contest I still go Sidious against Dooku however the degree to which he wins is smaller than if he were higher up with his power.
Round 2. Dooku is a great politician, and will be rembered. However Sidious was the Sith Lord and rallied Dooku to his cause and he told Dooku who to rally and influence half the time and he worked his way up to Empeor of the Galaxy. So really Sidious wins both rounds.
Either Sidious is brought down to Count's level, or Count is brought up to Sidious's level. So long as their powers are equal, I don't care how you choose to view it.
Registered: Feb 2015
Location: Heavens of Mystic
The Birth Place
Still Sidious. He was able to go toe to toe with Yoda in "disadvantaged" position, able to be the equal to mace Windu, disamred maul, and defeated savage at once. While I understand this Sidious will be on even playing field with Dooku, I'm not sure Dooku could replicate all of these.
It also comes down to creativity with the force and timing. Whoever uses it the best will also have an advantage since neither will be able to overpower the other in sheer force strength.
Round 1:
This is interesting. It would be a very good fight either way, but I think I might be inclined to side with Dooku in the end.
Round 2:
Again, this is an interesting question. Dooku single handedly(for the most part) rallied tens of thousands of systems to his cause, with nothing but his sheer charisma/cunning. That's huge. But then again: Palpatine rallied the entire damned Republic(and Dooku) to his cause, so meh. /shrug
It's actually a pretty interesting thing. If we are to state that their Force connection is completely equalized, it basically means Sidious's power is downgraded to Dooku level, while Dooku doesn't suffer any change.
Besides the fact that subconscious Force connection dictates impossible amount of things one would deem part of the raw lightsaber skill, we also have Dooku fighting at his normal that he's used to, and Sidious suffering a degradation he never had before, to the levels that were far before TPM. His shrinked Force connection would be on the level he never felt for so many years, so it's quite easy to say he would be at a huge disadvantage.
Not to mention that with perfectly equalized stuff attributing to Force connection, all that would remain would be the raw skill and actual experience.
Then again, Palpatine is younger. Dooku's Force amplification serves to diminish the hindrances of his own body, while Palpatine's physical hindrances are lower. The same amount of the Force energy given to the two bodies, one better, one worse - I don't have to say what the outcome is.
But in the end, Dooku - he would fight as his usual, while Palpatine would have to adapt to the lower level he is not used to.
Yeah, in that case it's Sidious who wins. Dooku would not be used to fighting at that level.
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Registered: Feb 2015
Location: Heavens of Mystic
The Birth Place
I don't think that would be an issue honestly. Both of them especially Sidious hold back to a degree. Sidious would most likely not have an issue since really he could fight like that since he holds back.
Dooku would not have any issue fighting on that level. He didn't have a problem fighting Yoda while he was amped IIRC. Beside form Yoda being more skilled of course.
I thought this would go without saying, but power equalizing does exactly what it implies: EQUALIZES POWER. Whether Sidious moves down or Count moves up, we are assuming they are fully acclimated to that level of power.