I know that 20amps is bare minimum for starting and operating a 13.5 AC. I can only imagine that you'll need at least 25-30 amps to get the 15k going. The newer style ones may be able to start on 20 amps. One spot I read, claimed 16amps for a Coleman 15k ac unit.
If all that is on is the AC, then either one is fine on a 20 amp house circuit. 15K BTU draws around (it varies with make and outside temps) 13A running, and instantaneous surge around twice that when starting. You can sometimes run a 15K AC on a 15 amp breaker, but sometimes they will pop after a while.
It very much depends on the design of the unit. For example my old RV had a 13500 air conditioner of the vintage of 2002. It would barely start on a 15 amp circuit. My newer RV the air conditioner is 2004 vintage--and it draws just 960 watts while running, so it easily starts on a 15 amp circuit.
Kustom Koach Class C 28'5", 256 watts Unisolar, 875 amp hours in two battery banks 12 volt batteries, 2500 MSW watt inverter.