I'm running a mismatched and staggered set of tires on my truck right now (by design) and have had good luck with each.
The front I have Goodyear Wrangler RT/S and the back are Firestone Destination AT
I had bought the GY's and had them on the back with the michelins still in front. I didnt like the look of the Goodyear's (too skinny and needed more traction due to so much HP from the twins) so I bought two Firestones (305/70/16 wider for better traction and larger diameter to increase top end) and put the GY's up front and the Firestones on back.
Since I have a two wheel drive I wanted the staggered look anyway. Both tires are E rated and handle fine. The Firestones have about 110lbs more max load rating than the GY's too. I tow a 10K toy hauler and have done so with each set on the back, The GY's rode a little harsher than the FS's do but that could be the way I'm pinching the sidewalls with the small stock rims and such a large tire.