doesn't have much to do with how it runs. in my area they just eliminated emissions testing on obd1 cars, i prefer them for modification reasons and so on. obd2 can be easier to diagnose problems, the computer system is far superior for that. obd1 codes don't always tell you much, obd2 codes are much more straight forward. obd 2 vehicles are more strict on emissions, so you're gonna get more o2 sensor, catalytic converter, evap and so on failures.
fyi, obd stands for On Board Diagnosis.