Bighorns will pail in comparsion to what you have been riding most of the time. Sure there are areas that are unreal, Wyoming T/A on here would be helpfull but if I was to choose the two you mentioned it would be the Snowies.
Now saying that why not try the Wyoming Range? They have the most snow of anywhere in the state on average every year. It's a further drive but less populated and more powder and more climbing.
I just don't think you will be too impressed with either the Snowies or the Horns if you have grown accustom to Togwotee and Dubois. Just depends on what you like to do I guess.
I stick with Togwotee, I have been going there before the cabins were built and still haven't found everything there is to find. The season before last when everyone was complaning about snow, we found some of the best stuff ever about 25 miles away from the lodge. It was unreal, went back last year and it was still untouched. That is why I keep going back to Togwotee, the are is just that vast.