Which car should I keep?

You answered your own question.you are on disability.neon 32miles per gallon.cheap for parts.you dont have much money to play with.

Plymouth Neons are really lousy cars and have many problems from head gaskets to overheating to transmission issues. The Toyota should be a much better car. I would keep the Toyota and hope for the best. The Neon will be trouble sometime soon.

the lack of routine maintenance on the Neon would be a deal-breaker for me. It's a ticking time bomb.

The Toyota will have better resale value even if the neon is newer. Make sure the starter is aligned correctly and that the voltage is correct at the starter if low voltage, locate the drain/short and put some electrical tape on wires rubbed bare. Make sure the ground wire is good Block to frame and battery to frame. Check the battery + terminal wire to starter. The Dodge neon is known for poor reliability. With either watch the temp gauge and do not let it overheat due to hoses, thermostat, ect which are maintenance items and replace when bad not after broken to avoid head gasket failures. Of course both are at the age to need more and more work, like brake rebuilds and suspension parts, axles, bearings. I keep one eye on the road and other on my temp gauge and both under the hood and the car looking for up coming issues. Now the condition on both cars as this can make you decide fast which to choose.