On most boards, but the amount is highly board dependent, from a small second-player advantage to a huge first-player advantage.
I'm speaking generally. In fact, I would pretty confidently say 2nd player advantage appears in Dominion less often than being out of position in poker ends up helping you (e.g. allowing you to raise before limpers can improve subsequent players' pot odds).
If you gave me a choice between random seating order for Dominion vs. letting me go first every time, I'll happily take the choice to go first every time! Maybe you could find a board where I'd prefer to go second (though I'm not sure I've seen such a board), but if those are my only two choices...
If you gave me a choice between the usual rules of poker vs. always being last to act before the blinds, absolutely I'd prefer to be last to act every time, even if being under the gun occasionally turns out to be an advantage.