Go back in time to the 'good old' (though not necessarily in all ways!) days of Benjamin Seaton and of Holtzappfel, and the 'carcass saw' was just a slightly bigger dovetail saw. I suspect the dovetail saw was used on small stuff (drawer sides and the like) and the carcass saw on thicker stock like - er - carcass sides. They didn't have any backsaws specifically for cross-cutting. They also had sash saws and tenon saws (which could be real monsters - Benjamin Seaton's was 19 1/2" long) for smaller and larger tenons. Most work was done by hand.
Fast forward in time to the middle 1980s, and there were two sorts of backsaw. The dovetail saw survived (usually with a very deep blade and a big, clunky handle), and the only other type was the 'tenon saw', about 12" (occasionally 14") with about 3" depth of blade below the spine, and a similarly clunky handle. Both tended to be supplied sharpened cross-cut. The 'tenon saw' was for doing tenon cheeks (very slowly) and for trimming pieces to length, often with a bench-hook, which it did quite well. The saw selection available reflected the fact that most work was done by machine.
Fast forward again to today, and there's been something of a revival in 'traditional' saw-making, so there's much more choice. It means you can suit saws to the type of work you do much more easily than in the 1980s. If you do a lot of trimming to length with a bench-hook, a cross-cut filed saw of 12" or 14" length, say about 12tpi, and not too deep in blade width below the back, would make sense. If you tended to do such trimming jobs by machine, maybe not so much.
I think for the general run of furniture-scale work, if I were starting again I'd go for a 10" dovetail saw, a 12" cross-cut filed carcass saw for trimming to length at the bench, and maybe a 14" sash saw for larger tenons. Unless you were doing large-scale joinery, that should cover pretty well all back-saw duties.
