For me, recoil pads are a must on target guns which get shot a lot. However, I do most of my upland hunting with Model 12s utilizing the original hard butt-plate. I like this because (a) I'm not shooting a ton of shells, so recoil isn't bad and (b) the slick plate doesn't hang up on my clothing when mounting the gun (often out of breath and off balance from chargin after the dog). When shooting magnum loads at waterfowl, I use a gun with a decent pad.
Recoil pads can be modified somewhat to keep them from hanging up. For example, the gun I use most of the time for sporting clays has a Pachmyar Decelerator pad. In its stock configuration, it would catch once in a while. However, I used a belt sander to radius the top edge of the heel, and a sanding block to remove a bit from inside the toe (just for a better fit). I then stole some of my wife's clear fingernail polish, and coated the edges of the pad and the radiused portion of the heel. This keeps the part touching my shoulder from slipping, but removes most of the potential for sticking to my jacket as I mount the gun.
BTW, recoil-reducers usually refer to something added into the stock, such as a mercury recoil reducer, "dead-mule" or such. There are a number of different designs, which do (or at least try to) two things. First, they add weight which helps cut recoil. The other thing is to alter the recoil impulse from a hit to a shove. The first is real and provable. The second is more difficult to quantify and the perceived benefit can vary among shooters. One thing they will do is change the balance of the gun. If you add one, you may need to play around with attaching some weight at the barrel, so as to restore the handling characteristics.
There's a very good reason why I do all the cooking around here. 
