I think Caesar's Legion is generally a lot more at home in the wasteland than the NCR. Tribes of psychopaths with spears killing, raping and enslaving anyone who aren't them existed in postnuclear America long before Edward Sallow started calling himself Caesar. He only took one such tribe and taught them how to be better at it.

I think Caesar's long-term goals for the Legion is to forcibly evolve them from a nomadic army into a real nation. The NCR didn't organically happen, it was planned and enforced by a core group of founders in an idealized image and that idealism failed in the face of reality, so the NCR turned corrupt and degenerate. Caesar wants to take Nevada and eventually California so that his Legion will finally run out of lands to conquer and be forced to grow up. He even designed their whole military doctrine in a way that the most fanatically devoted members of the Legion are also the ones most likely to die and make room for calmer heads in the end that can reshape them into their final form.