So OK, let's consider a very simple scenario in which both players' first four hands are identical, and the only action cards of interest in the early game are Chapel and Lab, but there's a Market and enough other stuff to make a killer engine.
They both open Chapel/Silver on 3/4. T3, both draw CCCEE and buy Silver. T4, both draw Chapel-SCCC.
Turn 4:
P1 Chapels 3 Coppers.
P2 buys a Lab
Turn 5:
P1 draws CE and 3 of Chapel-SSCCCEE (8 cards)
P2 draws CE and 3 of Chapel-Lab-SSCCCCCCEEE (12 cards)
One thing we see immediately is this: P1 will get to play Chapel again on either T5 or T6. Their deck has 10 cards. P2... might not see their Chapel until T7. But hey! Let's just assume best-case scenario for P2 and worst-case for P1. So:
Turn 5:
P1 draws CCEEE and buys nothing
P2 draws Chapel-CEEE and dumps four cards.
Turn 6:
P1 draws Chapel-SSCC, dumps the Coppers. Buying another Silver would be counterproductive at this point.
P2 draws Lab-SCCC, then draws CC and buys a Gold (or, say, a $5 with +Buy, like Market).
At this point, our status is this:
P1's deck is Chapel-SSCCEEE
P2's deck is Lab-Chapel-GSSCCCCCC, and is guaranteed to draw SC plus three other cards next turn.
P2 likely has an edge here because they got rid of all their Estates and P1 failed to get rid of any, but the chance of P1 not getting rid of some in the next few turns is pretty low.
So if we give our trasher the worst possible outcome and our buyer the best possible outcome, the buyer comes out ahead.
What about the reverse?
Turn 5:
P1 draws Chapel-CEEE and trashes it all.
P2 draws SCCCE and buys another Lab, or a Market perhaps.
Turn 6:
P1 draws SSCCC and buys a Lab
P2 draws SCCEE and... probably should skip another Silver buy.
P1's deck is now Lab-Chapel-SSCCC
P2's deck is now Lab-Chapel-Market-SSCCCCCCCEEE
P2 is guaranteed to draw Lab-Chapel-CC and will definitely finally get to trash some cards on T7. But their deck is 15 cards thick, and P1's deck will hit $6 or better until they start greening.
P1's best case scenario is hugely better than P2's best case for moving into an engine.
P1's worst case scenario is certainly better than P2's worst case, though likely not by as much.
P1's average case, then, is better than P2's average case.