In California you usually get to keep you prop 13 tax base if you move. Your new home has to cost less than the selling price of your old home. No penalty.
Only if you stay within the same county or move to a county which has voluntarily adopted Proposition 90.
There are several nice counties that accept prop 90. San Diego, Orange, Alameda, Los Angeles, Santa Clara to name a few. Combine that with the fact that you can downsize in your own county and the penalty can pretty easily be avoided.