The Ford Mustang and the RX-8 are two different cars for two different purposes. The Mustang is FINALLY getting an independant rear suspension so that will help its handling, but will never change it's characteristics -- it's a pony car, muscle car, whatever. It's a straight line rip-and-roarer.
You must also take into the fact, the base Mustang is going to come in at ~20k which means it will be extremely popular in a short amount of time. Even if you get the top of the line, decked out model, your car will be all over the road, so you will lose 'exclusivity' in that regard. Additionally, Ford has never been good with their interiors, and since the Mustang isn't really top of the line (ie, Lincoln, which also sucks) your interior is going to suck, be low quality etc. The back seat of a Mustang is useless for people, it's fine for groceries. Just incase that was important.
The RX-8 is a more well rounded car. I've sat in one many times, and you can easily fit a 6 foot person up front and one behind that. Granted it's no Caddy with space, but for <1 hour rides, I don't think it will be much problem for anybody. Of course, if you sit gangstah style then obviously you won't get anybody behind you. If you want straight line power, the RX-8 is not your car.
Also to those rotary bashers -- they don't know a damn thing about auto mechanics. Rotary engines almost never fail. Neither do conventional piston engines either, for that matter. When's the last time you went to the mechanic because "my engine died"? It's rare -- and besides the fact that the Mazda has a 5 year warranty, I don't think you have to be worried about that terribly. The rotary engine of yesteryear that was so problematic was because of the 3rd generation RX-7 and its turbos. The turbos introduced a great amount of heat into the engine which cracked the apex seals -- the things that keep compression in the engine. The turbos were remedied in Japan, where the RX-7 sold until last year and met very high reliability standards. If you were buying an RX-7, I'd say to watch out, make sure you get a bigger radiator and cooling equipement... but with a naturally aspirated rotary that's of little concern. If you are still worried, then buy the Mustang with the lower warranty and lower quality parts.
The RX-8's shining light is its handling. The rotary engine is beneficial most in this, because it weighs very little. The torque is low to be sure, but the horses are good and compete with the 3.5L V6 from Nissan/Infiniti, at a fraction of the weight. Additionally, the engine is mounted ENTIRELY behind the front axle so the weight balance in the car is excellent. Let's not forget, the base model weighs under 3000lbs, and the loaded one just a hair over 3000. The Mustang if I had to guess... to put out that power.... at least 3500-3700 lbs. This is what makes the G35C and Nissan 350Z so tiring to drive... the cars are heavy and don't handle as well as the light and nimble RX-8. There's a tradeoff as I mentioned, in power... but the fact I can tote four people around, use the car competitively on an auto-x, and still have enough power to beat 99% of the cars on the road would make me happy.
So what does it come down to? Power - Mustang. Handling and semi-practicality - RX-8.
You decide.