Actually, I suspect the Eschaton that Charlie Stross writes about is probably more powerful that a Culture Mind as it appears to use time travel for computational purposes:
See also Scott Aaronson, Quantum Computing Since Democritus, or the lectures on which it's based[1], or his paper, "Closed Timelike Curves Make Quantum and Classical Computing Equivalent".[2]
In Consider Phlebas, the refugee Mind that was hiding in the tunnel system was described as existing mostly in hyperspace [1]. Whether that beats time travel as a computational shortcut I really wouldn't know.
http://www.antipope.org/charlie/blog-static/2010/09/books-i-...
Of course, proving that the Eschaton is more powerful than a Culture Mind (or one of Vinge's Transcendent Powers) might be a bit tricky.