[...]I was saying Bridge is better at exploding because for exploding, getting $ a turn earlier is a huge benefit.
I don't think this is always true. Say the goal is to buy that big expensive victory card (this applies so far to BM or engine). It doesn't matter what your previous buys do as long as you can get Provinces in the end. You use Merchant Guild to save up a stash of coin tokens and then spend them all at the end to get expensive victory cards.
So your second-to-last shuffle looks the same only this time, whether you're playing money or engine, now instead of having a deck full of action cards that you *have* to play in order to kick off, you have a reserve of coin tokens, which is much more flexible.
But coin tokens are at their worst in large quantities
...unless you have some +Buy to use them with. With MG and nothing else in hand, you can double-province with tons of coin tokens in reserve.
A massive reserve of coin tokens and a deck with +Buy cards is a constant threat to at-least-double-province every turn without the risk of a bad draw. This gives you nearly complete control of the end game, and I think that's very powerful.
...Of course everything I just said based solely on my own experience so I could be wrong.