I have both - Piettas - stainless .44 and blued .36. While I enjoy shooting both, I much prefer the Navy caliber "just because" - i.e. a personal preference.
To answer your question - I've never done penetration tests, etc. with either. I would imagine the .44 would probably give a little more "umph" just because the ball is larger and a larger powder load. (I'm comparing apples to apples - steel frame to steel frame).
Maybe someone will take issue and correct me - which is fine as I'm always open to learning.
Between the two calibers though - I'm thinking in rifles - I've always had better luck with a larger caliber - say a .32 compared to a .45 in regards to how conditions affect them. I'm talking such things as cross winds, etc. Whether that transfers to the two pistol calibers I can't really speak to as I don't shoot long distances with my revolvers. Between the .36 and the .44 - it's not really that great of a difference as say rifles in smaller calibers and those in larger calibers.
I'm also thinking about generations past as well. My favorite revolver is the '51 Navy. Colt obviously sold a lot of them not only for military but civilian use as well as they were manufactured up in to the 1870s. I suppose that in regards to your thoughts - you would select the caliber that is going to fit your needs the most if you are going to hunt with it. Smaller game the .36 would work fine - larger game such as coyotes, etc. I personally would choose the 44 over the 36. Remember though . . . . in years past when these guns were in wide use, a .36 would kill a man just as easily as a .44.
As far as expense . . . yea, the .44 ball requires a little more lead and a little more powder - but not that much to where I consider that to be a part of picking which one a person wants. You still have to use a cap with either.
My Remmie Navy is the same frame as the bigger brother 44 but I find it to be well balanced. Of the two,I still prefer the '51 Navy as in my hand, it feels better but again, that's a personal thing.
Kind of like "modern" handguns - I much prefer shooting 38 spl over 357 and 45. Probably because I'm getting old and it's more comfortable for me to shoot?