The padded seats can be more comfortable, especially for elderly people who are uncomfortable sitting on hard surfaces. Over time, a padded seat top may become worn out or split, they could be replaced if necessary.
Phenolic seats are often available in more color options or a wood grain look, so they tend to be more aesthetically pleasing, and they are more durable in the long run.
Each of these materials have pros and cons, and it really comes down to customer preference.  Both seats are waterproof and easy to clean, and the frames are usually exactly the same.