The question is how soon can you get such an engine up? And what route do you take double-tact with? Tactician and Count makes for a great way to thin, and Count provides some virtual money, but I'd imagine you'd want to transition into Soothsayer and Butchers, meaning you'd probably want some Wandering Minstrels too to sift (Yeah, University is +Actions, but it doesn't draw for you). Stonemason can get multiple $5 by hitting $7 or by trashing the Golds gained from the Soothsayer, and University is a help for getting $5. Unfortunately, there's not much in the way of draw here aside from the Tactician of course, so you'd have to trash down enough to where the engine is reliable. Even more unfortunately, the only way to quickly trash down is Count+Tactician, and Count can only spare two cards so you'd have to trash first and then build, but you're getting hit with curses the whole way. Even if it does come together, that still takes time to get all 8 Provinces (especially if you're without Wandering Minstrels to sift; your double tact engine is going to get gummed up with that much green, thin or not).
Meanwhile, the slog has so many things going for it. Gardens and Count work amazingly well together, Soothsayer adds cash and cards for the Gardens player, Stonemason can quickly three-pile in a pinch, not to mention the extra gains...I mean, it's hard to argue against a strategy that won, especially if the player is WW. Of course, 5/2 is so good here for the first Soothsayer.
If it's double-tact engine vs slog and I had to play the engine, I think I'd have my work cut out for me. I'd have to contest the Gardens and the Duchies while somehow getting Provinces. Stomemason can help get my $5 components quickly of $7 (pretty easily reachable with the Golds from Soothsayer), and can later trash those Golds for Duchies...but I'd probably just Butcher them into Provinces instead and let my Count grab Duchies for me (although I suppose if I could cut off his Duchies quicker, that would give me a better chance). I probably wouldn't want to help empty the Estate pile however; I'd be choking on green as it is, and it would really only help my Gardens opponent. I think time is going to be a major issue: your engine has to be about ready by the time your opponent goes for Gardens so you can contest them, and on this board, that's not very long at all.