I think the usual engine-driven underhood unit would be rated at 20-30 thousand BTU. This jibes with the rule of thumb that it takes maybe five hp or 3.8 kW to run the thing. That guesstimate refers to the modern cylindrical compressors with helical innardds of the fixed-displacement kind usually used in the US. I think the old-fashioned ones that looked variously like lawnmower or mini Harley engines took more like 10-15 hp.
Why so much (2-3x the BTUs of a window unit for the home)? A car may be small, but it has a lot of glass and tends to be parked and driven out in the sun, which means a lot of radiative transfer in and a tendency toward trapping that heat.
(An interesting sidelight, no pun intended and probably not much of one achieved... Some recent research, oriented toward quantifying how badly things go wrong and how quickly when you leave your kids or pets in a parked car, indicates that not only is the heat gain is at least
40-50 deg. F over ambient, but a large part of it happens early on.)
Various companies and institutions like the National Renewable Energy Laboratory put a lot of research into these things because it's one of the areas where small improvements in system efficiency or need reduction, times a large fleet, equal big savings.
Again, that refers to the typical underhood, belt-driven unit. Auxiliary ones that you see on the top of motor homes are usually about
12-15,000 BTU each, two or three units per vehicle, and run off of 110V a.c. house current rather than the vehicle's 12 V d.c.
Cheers,
--Joe