Ignoring physical pain, is it better to use rubbing alcohol or hydrogen peroxide to clean small wounds?
I think alcohol is better than peroxide for the reasons stated above.
Nevertheless, from an evidence stand-point, there is no really strong evidence for basically any solution over the other or even for whether to clean or not clean wounds.
Personally (and what is preferred by most in daily practice and generally recommended in guidelines as well) is cleaning with a running solution (either isotonic saline or water) as it's believed that the largest part of the cleaning is actually done by mechanically pushing the germs off the wounded region.
Considering this source, hydrogen peroxide is not only ineffective it is also slowing the healing process down. It causes damage to your own cells.
Alcohol also damages your skin cells. But at least it minimizes germ activity.
So alcohol is not as bad as hydrogen peroxide, but it is better to use a different solution.