Borgata used to be owned 50/50 between Boyd and MGM, but that is no longer in effect; Boyd's only Vegas casinos are not anywhere that the Borgata clientele is likely to be interested in, and they have a separate player's card anyway. You could try seeing if any of the casinos would give you anything for your black card, but the matching programs are mostly an AC phenomenon, and the Vegas casinos likely look down on AC anyway (and are unaware that the Borgata is actually fairly nice) so it would be hard to convince them just by showing the card that you're worth anything.

That said, if you play enough to be Black Label, and if you go to Vegas and focus your play on one brand like MGM Resorts (which owns Bellagio, MGM, Mandalay, Mirage, and others), it shouldn't be hard to start getting comps there as well, and they will likely be willing to retroactively comp some of your room charges at check-out if you play at the same company's properties as where you stay, and if you play enough during your stay. In general the nicer Vegas properties are much stingier with free room offers to low- and mid-level players than the Borgata is, even on weekdays, but at the least you'll get discounted room rate offers and the potential to have the room comped at check-out.

The only brand that will seamlessly give you credit between AC and Vegas is Caesar's (Harrah's) Total Rewards, but unless you're a slot player that's not likely to be a good choice in general.