Oh, goody. I suspected you were aware. Now, I know the meaning of your question.
OK,--the blackpowder versions will get more power in longer case lengths, hence, the 3 1/4" version will be more powerful than the 3" or 2 3/4".
HOWEVER, the nitro versions of 3" and 3 1/4" are the same power, only the 3 1/4" works at lower pressure.
The 2 3/4" version nitro is lower in power than both the 3" and 3 1/4", and usually, but not always carries a 650 grain bullet instead of the 750gr.

As for case availability,---now that Jamison Brass is in almost full throttle turning it out, it is a lot easier to get than before. Jamison has 2 3/4", 3", and the 3 1/4" version available, and can be ordered from Buffalo Arms. This is where I get my 3" cases. All of these are usable for not only nitro, but blackpowder as well, in other words, they do both. It may have the headstamp as .577Nitro, but loaded with black, and the proper bullet, is essentially the Blackpowder Express loading.
I've had good luck with Jamison brass, and it is top quality in my opinion.
Of course, Bertram makes it too, and is also offered, but it is of varying quality, and more expensive, which does not reflect it's quality.
Also, A-square, but I would be cautious of them, as they have reportedly soft brass of varying quality also.
Also, Horneber, which can be found at Huntington's, MAY have the .577 in the line-up.

To close, I would say either Buffalo Arms, or Huntington's, can supply any needed cases.

Also, sorry for the confusion in questions. I figured you knew all of that from the start, it's just that, here on the net where no-one can speak in person, I like to cover the bases due to safety's sake. Hope you did not mind. I assure you, I was not speculating on your knowledge of the issue.

p.s.---bullets....bullets are available from Midway, and Huntingtons, however, Buffalo Arms does not carry them. Woodleighs, or Barnes. Although if firing a double, I'd not use Barnes.
Again, I'm sure you know this. Just wanted to add.