1. By "bloodlust" do you mean both are sort of mindlessly focusing on killing each other without any real strategy beyond, say, the actions taken by Superman in Greg Rucka's "Sacrifice" battle against Wonder Woman?
Or do you just mean "These guys are fighting in character, perhaps even strategically, but are resolved to make sure the fight ends in the death of their opponent"?
The first kind of fight would much like the following:
... and that type of fight would probably either split or be in Black Adam's favor (given Adam apparently had multiple series of that type of engagement throughout the World War 3 storyline).
On the other hand, if Beta Ray Bill, more used to fighting exotic menaces than Thor (I imagine),
is likewise more given to using the exotic powers his hammer, Stormbreaker, grants him to meet those menaces,
... then I see Bill able to score an easier knockout against Adam than most other heralds.
You can go with either your second option of which they are still mindful enough to use all their powers strategically or go with both scenario's, your choice.
If we're going with option 2, any Thor class character that is thinking strategically and has even an inkling Black Adam is powered by magic LIGHTNING, is going to use their Uru hammer to block or remove Adam's power.
The images I've posted before now (with, of course, the exception of that kamikaze rush) all display "Thor-type character probing magic-empowered character and then blocking or removing magic-characters power", an inherent ability of Mjolnir and, presumably, Stormbreaker.
Thor figures out that Captain Marvel, for instance, is powered by the Shazam lightning, in DC versus Marvel #2. So he instantly moves to intercept the bolt, and does, and we get some weird results here, presumably so that, 4th Wall, we can have Wonder Woman cosplay in the next issue.
The point, however, is that, being more or less MASTER of most forms of lightning, Shazam characters are a threat to strategic Thors only when they allow them to be. At least, of course, if the abilities of their Uru hammers are allowed.
Now, of course, the objection might come "Thor stopped that bolt en-route". That's why I posted the page with the Wrecker.
It demonstrates that Thor can remove or redirect magic power ALREADY CONTAINED in a person's body. Or even that of several people at once:
As to the objection: "Unless Adam transforms or uses the lightning, Beta Ray will have no way to know Adam's power is magic"?
That's what the Juggernaut versus Thor showing was about.
Wondering exactly why Juggernaut is so tough, Thor simply makes Mjolnir examine the nature of his invulnerability, concludes it is magic, and then has Mjolnir block it accordingly.
(I posted/am re-posting most of the scans after that scene simply for fan/reader enjoyment)
Ditto man, This would be one hell of a fight, and it's too close to call. Soon as I think that one of them wins, I remember what the other can do. Split.