There are so many diverse opinions on the subject that I hate to get into it.
If you are talking about suspension bushings such as the inner lower A arm pivots on a Healey, I feel that the conventional steel sleeve bonded rubber type is the best. The metal parts of the bushing are firmly clamped mechanically & rely on twist (torsion) in the rubber for movement. They obviously don't require supplemental lubrication.
Poly & nylon bushings are not bonded & rely on movement between the bushing & the adjacent metal. They usually require lubrication which is not provided for. These bushings are often available in several hardness grades.
For bushings that do not rotate, either will work. Rubber gives the softest action. Stiffer bushings also transmit more force to the mounts & put more stress on the attaching parts.
For "race" bushings, where things are frequently replaced, disassembled for regular maintenance, ect., hard bushings are favored for the last little bit of control precision,-- maintenance, mount stress, noise, harsh ride, are secondary.
Since so much of it is personal preference, I think you will just have to go with what you think is best. It can always be changed back if you don't like the result.
D