As for range... remember that every V-22 variant (including the CMV-22B) is equipped with a retractable refueling probe - thus its actual range is "tanker availability/crew endurance/engine run-time".
Note also that the C-2 Greyhound was NOT equipped for mid-air refueling (although this could have been easily done).
The CMV-22 actually has a higher max internal cargo weight than the C-2A* (even though a smaller internal volume) - and the height/width of the cargo compartment is similar** but not identical. The higher ceiling in the CMV-22B means that some cargoes fit in there that wouldn't in the C-2.
Neither can carry an assembled F135 engine in its shipping container (only the proposed CS-3 Viking could have), but both can carry all sections of a F-35 engine - including the lift-fan of the -B - in an open transport frame (which has been developed and tested), just not fully assembled.
They have similar cruise speeds (V-22 241kt, C-2A 260kt), and the CMV-22 can operate off a larger set of ships - all helo-capable amphibs, as well as flight-deck-equipped destroyers, etc - meaning many cargoes would not have to be landed on a CVN then transferred to an H-60 to be taken to their destination ship.
Yes, the CMV-22 has only a 26,000ft service ceiling compared to the 33,500 of the C-2A.
* C-2A "max useful load" (including fuel) 20,608lb; max cargo weight from land 15,000lb; max cargo weight catapult launch 10,000lb
V-22 max cargo weight 20,000lb internal, 10,000lb slung load single hook, 15,000lb slung load dual-hook
A comment on max cargo weight - this is where mid-air refueling helps. Many aircraft (fighters, transports, etc) cannot take off with both a max fuel load and max payload... either they take off with full fuel and reduced payload or full payload and reduced fuel. If you do the latter in the CMV-22B, then you just top off from a tanker once airborne.
** C-2A cargo hold
Length: 27 ft 6 in (8.38 m); Width: 7 ft 4 in (2.24 m); Height: 5 ft 5 in (1.65m)
V-22 cargo hold
Length: 24 feet, 4 inches (7.41m); Width: 5 feet, 11 inches (1.80m); Height: 6 feet (1.83m)