Levshunov's a RD, has more offensive talent and is more punishing physically and in front of his own net, if way more inconsistent and raw than Dickinson. They're of different molds, but I'll likely have them back-to-back in my ranking.
If we had to compare Dickinson to a player who I'd consider to be more of the pinnacle of his own style, and a true 1D, it'd be Ryan Suter. I don't think Dickinson's defensive instincts and potential are quite as high. I don't see him as a primary shutdown defender, though he could be a part of a shutdown duo as you pointed out with Reinbacher. But true #1s can carry lesser partners (Komisarek, Gorges, Chiarot) on a top pair and I don't see that in Dickinson's future.
As far as Markov is concerned, he was a savant, and a purely cerebral player. Dickinson's relies much more on his physical tools, and does not have anywhere near the same vision or IQ.