I remember reading that there were quite a few elderly Texans moving to California for a reason that you probably would not expect: taxes.
Texas does not have a state income tax. They make up for that with high sales tax and high property tax.
California does have a state income tax. It also has a high sales tax, which is about the same average rate as Texas (the state rate is lower in Texas but local rates are high so it comes out about the same). Property taxes are lower in California. It is #16 among states when sorted from low to high property taxes. Texas is #45. Rates are about 2.4x as high in Texas.
Thus if you are a retired homeowner in Texas considering moving to California it comes down to whether the lower property taxes will outweigh state income tax.
California state tax does not apply to Social Security, so if your income is mostly that and low tax investments (like a Roth IRA) it can quite easily turn out that you won't pay much if any California income tax.