Depends on where they are. If they're in BH's realm, or any other part of Hell, he takes it without too many problems. If they're on Earth or something, I'd say about an even split.
In a fair fight I'm going to pick Thor everytime. Blackheart's an impressive demon but he's not all that major and powerful compared to the higher end demons. Can he lead a pocket dimension hell for awhile sure but odds are he's going to be overthrown a bunch of times. He's been beaten by a lot less then Thor and that's in his own realm. It's a nice fight though and even if the fight's set in a pocket dimension I'm still picking Thor for a majority. Thor does have some experience forcing his way into dark realms and running amok.
Blackheart isn't Mephisto, Satannish or even Hela more middle management like a Hellstorm or Belasco type. Blackheart could call up a horde of demons to help turn the fight but I think he needs help to take on a Thor level character. Just my opinion, I'm just not overly impressed with Blackheart.
... Actually, Blackheart is more powerful than Mephisto and probably a notch below Dormammu. Not only that, but he easily ripped a planet in half with his telekinetic powers. He also simultaneously controlled 12 million minds. How resistant is Thor to telepathy?