At the risk of being stoned by AA's Texas fans
I'll suggest that So Cal is more expensive no doubt about it but 2x? I doubt it; particularly if we are talking about a modest apartment in both places. One of the biggest (if not the biggest) differences in cost of living is real estate. IF you not are talking about buying a house that someone in AA's tax bracket could afford that gap shrinks dramatically. Not to mention the rental market is very renter friendly right now.
Similarly those online cost of living indexes or "calculators" are no more than "directionally helpful" -- there accuacry varies widely depending on individual cirsumstances