In order for a tire to maintain contact with the pavement in rain, it has to displace the water as it rolls. Assuming forward motion, the water gets pushed three ways -- forward, and to both sides. Of course, any water pushed forward is waiting for the tire to catch up, and that's what causes hydrplaning ... if the water can't be displaced as quickly as it builds up, the tire rides on water instead of pavement.
Obviously, with a wider tire there are two problems. First, the water at the center has to go farther before it reaches the edges of the tread. Second, there's more width so there's more water. A good tread design can help offset this by providing channels for the water to run through while the tread lugs (blocks) stay in contact with pavement.
How this translates into your situation is that your new tires are 2" wider than the old ones, so they have to deal with more water. Unless the tread is more effective at water dissipation, they won't be as good as your old tires in the rain.
<EDIT>Just went to the Cooper web site and looked at the STT. Seems to be intended as primarily an off-road tire. It has very little siping, which are the smaller grooves in the tread lugs intended to help squeeze water out from under the contact patch. The Dunlop Radial Rover is more of an all-purpose, all-terrain tire that is intended for highway use as well as off-road. Don't know but it would not surprise me if the STT uses a harder rubber compund for durability in rocks, and that won't help wet traction, either.
I guess you just need to slow down at puddles.</EDIT>