There are now three medium-frame Blackhawks: all of the 44Spl variants, the special-run 45LC/45ACP version and the 50th Anniversary 357Mag Blackhawk Flattop of 2005, from which the later ones were derived. In other words, take a 357 Blackhawk Flattop and re-chamber it in 44Spl, you've got the same gun as the new 44Spls.
These are the same strength as the New Vaqueros in the same calibers.
There have been successful re-chamberings with the stock 357 cylinders to 41Magnum (six shots) which tells us that these aren't exactly weak guns. The 45LC/45ACP flavors can take about 21k psi, which is enough to drive a 250gr hardcast to 1,000fps or so or a 200gr JHP to 1,100.
You can deliver more energy in 44Spl by a bit due to the thicker cylinder walls. Yet more again in 357Mag, if you like flinging light bullets fast.
From all the research I've done, these guns are all slightly stronger than a post-WW2 Colt SAA. Not by a lot...you generally want to stick with loads known to be safe in those guns.