I personally don't like training with padded weapons. There's something about getting whopped on the head or hand with wood that makes you try to be more careful in the future. I guess the closest thing I use to a padded weapon is a shinai. But those suckers can STING! I had welts and bruises all over me after my last testing. Brown belts and above have to go through this test of stamina and endurance while doing a kata. You get punched, kicked, and beat with a bamboo shinai. I remember one guy's feeting getting slid back several inches on the carpet from a HARD punch to his solar-plexus.
Me personally, it doesn't bother me getting hit while doing weapons sparring. (To a certain extent of course) I'm NOT about to go at it freestyle with a hardwood bokken. So, a softer material IS prefferable, but I would rather spar with something that does hurt and leave a mark if I make a mistake and get hit.
But, to each his or her own....
"One Mind, Any Weapon"