What makes a comfortable wheel?

I see two possible explanations. One is psychological and one is physical.

The psychological one is that these are the new toy, so you want to find a reason they are good. This effect is much more powerful than most people are aware of, let alone willing to admit. It validates your decision to buy those wheels. If you want to disprove this, you can hide all the distinguishing marks on the wheels (very hard) and see if you can tell the difference.

The physical explanation is that you can find a transfer function from vibrations on the ground to vibrations on the points you touch the bike, the saddle, the handlebars, and the pedals. I suspect the saddle is the most important as you have your legs and arms to damp the vibrations from the others. The wheels only contact at the ends of the axle, so if the frame damps some frequencies we can ignore those. A more rigid wheel will transmit higher frequency vibrations to the frame, which will show up at your contact points unless the frame damps them. There is a belief in the community that rigid is good. Generally, a more rigid wheel will absorb less energy in flexing than a less rigid wheel.

The energy lost in the flex of the wheel is one part of the rolling resistance of the bicycle. There are many others. At normal riding speeds air resistance is dominant so reducing rolling resistance is not as productive as it looks. If you are a racer a tiny edge is important. As a recreational rider, I would like a comfortable ride.

All of this doesn't answer the question your are asking-how can I look at the specs of a wheel and identify the comfortable ones as opposed to the harsh ones. I would have thought most of the damping was in the tire, so there wouldn't be much difference in wheels, but I haven't tried any besides the ones my bike came with. I suspect on average you will get more comfortable wheels if you buy cheaper ones, but that is based on my thought that high end wheels are oriented for racing, so want to minimize energy lost at all costs.

Internal rim width difference would change the tire profile, and thus volume as well as the direction force is put on the casing, which could have a significant effect on how/how well it dampens vibration. A difference in the volume of the rim well is also going to change the air volume of the "tire" (tube) which will have an effect. Side note: tire width does not necessarily increase monotonically with rim width.

I'm on the skeptical side of a wheel being a factor; as I see it any room for vertical compliance would also be room for horizontal compliance, because the force can be distributed along only one side instead of symmetrically. So if there were vertical movement to absorb bumps, there would also be tail flop from pedaling or in turns. In practical terms just consider the magnitudes; the only thing significantly moving between the saddle shell and the road is the tire rubber, followed by the seatpost if it is round+has a lot of extension... maybe the saddle rails? If my rim was noticeably moving in any way other than around the hub I'd be alarmed, not comforted.