What are the chief differences between the Ruger New Model Blackhawk and the Super Blackhawk?

The super blackhawk is 44 mag

Probably going to have to be more specific. There are various models of each. Clayton is correct that the super is 44 mag, however there are some new models that are also 44 mag. The difference being that the entire platform of the super is meant to handle that caliber.
If you want to compare specific models that would allow for a better answer.
If you want to know more of the history and why the Super was designed, I'd be happy to expand on that info as well.

There are a couple of versions of the New Model BH, the newer one is smaller than the original and has a little less steel around the holes so you can't run them as hot as the original New Model. The Super is pretty much unchanged and can handle just about anything you want to feed it, as you can with the origainal New Models.

The only New Model Blackhawk® you can get in .44 Mag is the Bisley Model with 7 1-2 in. barrel. The difference is you can not mount scope on the New Model Blackhawks like you can on the Super Blackhawk Hunter and Bisley Hunter. Click below to see the New Model Blackhawk® Bisley in .44 Mag

New Model Blackhawk Bisley

Steel grip frame on all of the supers also.

Don't like the lock under the grip, never use it in a 100 years. Gives me a reason to convert to a Birdshead down the trail.

I've been looking at the New Model Bisley in 44 mag and 45. What kind of pressure can they stand in comparison with the Super Blackhawk

Same frame, same capacity.

Yep.

As they say at that place where I get the fish wraped with the rice and seaweed--

Same-ting Same-ting-- Same-Same