Usually not bad, the nice thing about the GPSDO over the normal ovenized oscillator is that you don't really have to deal with long term aging and drift, since it effectively works itself out. Often a decent commercial surplus GPSDO will use a good OCXO, though not often a double oven in my experience, but even a moderate single oven will be good to around 10^-9 in short term stability, wheras any of them will be 10^-7 or so for a year of aging... so the GPS signal keeping it adjusted will keep your reference much more accurate compared to 'absolute' time as you use it - even the best ovenized oscillators don't match their normal short term spec with their aging characteristic, so the majority of the error is going to be that aging drift.
Especially with the easier to find GPSDOs, there is often good analysis from timenuts around the web with good measurement equipment, so take a look on ebay and see how the performance may be. Usually these used telecom GPSDOs start around $50, and because they were originally designed for important timing applications, their oscillators tend to be fairly good. The really top notch oscillators may not be that cheap, but a nice single oven will probably be in range.