Mileage wears out the parts made of metal:
pistons, rings, transmission parts, bearings, power steering, AC compressor, metal suspension joints, CV joints/differentials, etc. It can also wear out the driver's seat and shock absorbers.
Age deteriorates the parts made of petroleum:
gaskets, dust seals, brake lines/seals, interior, coolant or transmission fluid hoses, air conditioning seals/hoses, insulation on wires, plastic parts, suspension rubber, fuel pump seals, etc. To be clear, these issues start appearing at around 15-20 years. Age can also cause rust inside the engine / head gasket and radiator or can cause the brake fluid to go bad if the fluids have never been changed.
Given the choice, I'd go low mileage. Most of the age issues are leaks/inconveniences which are cheaper to deal with (or ignore) than a worn out motor or transmission. Replace the hoses, flush the fluids, new plug wires, and off you go. Aged cars also feature lower insurance, lower tax rates, and cheaper parts, regardless of your particular car's mileage.