First I want to make a few assumptions:
1) We're playing Basic Big Money + X. We buy Province with $8, Gold with $6, Silver with $3, nothing with $0. We buy two copies of our chosen card at it's price point over any respective treasure (e.g. with $4 or $5, we buy Smithy over Silver until with have two Smithies).
2) All cards are fair game for choosing, provided they can be bought from the supply.
Now the reason I stated explicitly it's basic BM+X is because, if you play BMU+X (Big Money Ultimate) instead, you can never get worse than just playing BMU. Why? BMU+X buys the optimal number of X, and if that optimal number is 0, well, that was easy. And I chose 2 copies of the specified card somewhat arbitrarily. You can't get all of them really, a Minion deck isn't exactly BM, and two I think tends to be about optimal for standard BM play. So considering those conditions what do I think?
I think it's probably a $6 card that's overall not very helpful - this means we'd buy it over Gold twice. Farmland or Fairground, most likely. Farmland isn't going to do much, trash Estates into $4s (we'd need to specify which ones), Fairground is going to end up worth 2 VPs and do nothing for us otherwise, what a waste of money. Border Village gets an honorable mention, as it close to turns our strategy into BM with two $6 silvers.
Of course, these rules are kinda arbitrary, and really I think a lot of cards end up being equivalent as BM+X strategies, which is 'don't buy the X'.
A far more interesting thing to look at would be which BM+X strategy does the worst under BMU conditions (optimal number of X buys) subject to:
1) At least one X must be bought (or at least must almost always be bought)
2) The BM+X strategy must beat BMU on average
Then you start getting something interesting - you're looking for cards that make BM better, but barely.
