I've flown with both airlines, and would happily recommend either one.

Basically, the difference is that Volaris targets cost-conscious travelers, whereas AM goes after a broader market, with offerings like business class service, airport lounges, and ability to accumulate frequent flyer miles. (As a result, that, combined with higher operating costs, means that AM's fares are usually higher than their two biggest competitors, Volaris and Interjet.)

Unlike U.S. carriers though, these three Mexican airlines all offer complimentary alcoholic drinks on board, and one free checked bag per person.

I haven't personally had the experience of flying out of TIJ, but I do know that Volaris has shuttle service (for a fee) between TIJ airport and San Diego (downtown Amtrak station, I believe).

That said, if it were me, I wouldn't have any issue driving to TIJ airport. The only thing that I can't speak to is the parking situation at TIJ.