Prop 13 dictates that property taxes can rise no more than 2% per year from 1978 if ownership remains unchanged (exempting offspring who inherit, who get to maintain this break). The 2% maximum annual increase applies to all properties bought after 1978.
If a property falls in market value below its assessed value, you can appeal it and get it lowered. But once its value climbs again the assessment can “catch up”, that is, go up in excess of 2% per year until it bounces up against the ceiling of “2% per year increase from date of purchase” rule.
So in the two examples you cited, yes, the two owners will end up paying different property taxes on properties with the same market value.
