Experience with a '63 no. With bushings yes.
Whatever you have heard is just some ones opinion. Both work. Polyurethane plastic bushings are stiffer than the rubber replacements available today. But then again the original rubber bushings from the factory were stiffer than what you can buy today. The difference is in how much the bushings will give when stressed, and how much vibration will be transmitted through them.
If you are building a restoration your choice is obvious, you want the rubber bushings. If you want more performance than the stock "Jet Smooth" ride that Chevy would have been better off calling Marshmallow soft. (this is because due to global warming air turbulence has increased in elevation such that were jets fly they can occasionally experience a rough ride). The plastic almost is an automatic choice. (in your '63 I would recommend the plastic). The reason for the discrepancy depends upon whether you have a Panhard bar to center your rear end or you have diagonal upper rear control arms centering your rear end. The diagonal uppers have to rotate in two planes and plastic can not do that, so you need either rubber or a solid steel ball heim joint to allow the control arm to articulate properly.
Plastic isn't as bad and some purists would have you believe. If you are like the princess that can feel a pea beneath twenty mattresses, then do not buy plastic bushings. If you can not hear yourself over your exhaust noise and the motor is bouncing from wheel well to wheel well, then go for the plastic: and definitely replace your motor mounts with plastic as the motor shouldn't move around that much and only rubber would allow it to happen. I used solid aluminum bushings in my Camaro and Nova street cars that I built to be able to race. I also used solid steel with roller bearings for mounting the upper and lower A-arms on the front end to limit defection when cornering (my hot rod street cars did more than drive in a straight line at the drag strip).
Using solid metal bushings are not for those that don't like to have a car that performs on the ragged edge. Definitely not what you want in a car driven cross country at any regular interval, as your arms will fall off from the vibration. But I have driven cross country with plastic bushings without any problem.
Choosing a bushing material is like choosing a muffler; it is going to be a personal choice, not a technical one.