If you're playing a Militia every turn and limit your opponent to pretty much Gardens buys with Woodcutters and Coppers thrown in, you can definitely outrace that with Provinces. Woodcutter/Gardens is really weak. Market helps it a little bit but probably not by too much. I'm guessing that a Gardens deck needs ~50 cards to be competitive if it skips Provinces altogether. Engine also the option to snipe a couple of Gardens whereas the opposing strategy probably can't snipe Provinces.
Village/Moat is functionally equivalent to a Lab with less reliability, but it costs the same amount of $ to buy. In the engine, you can probably build to a deck state of 3 Gold, Militia, and 2 Market, then buy Province, Village, Moat every turn until the game ends, maybe transitioning into Province + Duchy in the endgame.