If I have a VOR receiver and a GPS, which should I use to navigate VOR airways?
will the GPS get me closer to the centerline, or the VOR receiver?

GPS is usually more precise than VOR. Even when selective availability was used this was true, and that program hasn't been in effect since 2000.
The GPS will also have approximately the same error along the entire airway. The VOR's error will increase with distance from the VOR station.
That said, IMHO there's a difference between &quot;which is more precise&quot; and &quot;which one should I use&quot;. Airspace features such as airways increase the chances of a collision by concentrating air traffic. An airway isn't as bad as an intersection or airport, of course, and flying appropriate altitudes for your direction of flight mitigates this risk even more. But I would tend to want to avoid being right on the centerline.
Many GPS receivers (and other RNAV devices) allow you to offset your course, so you can fly the airway that way, with a randomly selected offset that remains within the airway†. Or just use the VOR, and let its natural lack of precision help you to avoid being smack where all the other air traffic that's flying exactly on the centerline is.
† Strictly speaking, one should request the deviation from ATC, to avoid running afoul of FAR 91.181, which requires flying the centerline…it is unlikely they would object, but if they do, then you will find out the safe way