I presume you mean "Chapel/BM and Chapel/Dead draw/BM are slower than Dead draw/BM"?
Since I'd be incredibly surprised if Chapel Bot loses to BM bot.
Either way, thank you for the illumination.
My original claim was that Chapel/Big Money will lose to Big Money + Envoy (or Smithy). Of that, I'm positive. Chapel/Big Money might even lose to pure Big Money, I don't know. The latter is closer.
The reason is because a Chapel/Big Money deck really hurts during the greening stage. The fewer cards you have, the more your purchasing power suffers from filling your hand with Victory cards. Now, a well-constructed Action chain can handle the Victory cards, which is why Chapel is such a powerhouse--it's the fastest route to such an engine.
But if no engine exists--because the available cards don't lend themselves to one--trashing Coppers and Estates unnecessarily slows you down from getting Silvers and Golds. And Smithy/Big Money buys 4 Provinces in 14 or 15 turns, on average. With Chapel, you'll be trashing between Turns 3-6, and then need another couple turns for money. Also, say you manage to tie it up. The Chapel/Big Money player will in all likelihood lose the Duchy dance, because his purchasing power suffers way more from additional greening, while Mr. Smithy/Big Money continues along merrily buying Duchies (Coppers aren't so bad for buying Duchies, after all).