I'm putting a 3 rotor twin turbo in my 914 (20b in Mazda speak) which the guys here are probably tired of hearing about.
I also have an 87 RX7 Turbo and am a member of most RX7 bulletin boards. A bridgeported n/a 13B is good for around 280 hp at the flywheel. The guys are right though in that rotories typically don't make a lot of torque. My 3 rotor is the rotary equivalent of a big block and makes 300 hp / 300 lb-ft of torque in stock form. With the overlap on a bridgeported engine you will get a mean sounding exhaust pulse that will gently rock the car on it's tires at idle (brapp...brapp...brapp...). The 20b sounds like a cross between a V12 and a Buick Grande National.
As for downsides the largest would be heat. Rotaries get extremely hot. Exhaust gas temperatures commonly exceed 900 degrees celcius. Overheat a rotary and you usually blow your water jacket seals and need a rebuild. They also don't handle detonation very well. If you mess up with the fuel mixtures the result is usually catastrophic engine failure. When apex seals blow you may end up with wrecked rotors, housings and turbos. For new engine parts you are limited to what Mazda has left in stock and a few independant shops. For comparison there are many more parts available for a Chevy 350. Good used parts are also getting harder to find as well. There are also a limited number of shops that can work on a rotary so be prepared to do a lot of work yourself.
The upside is that they are hard to beat in terms of power output for their size and weight. If built and tuned correctly they can be made very durable. A rebuild runs in the $1000 range if you can do it yourself or $2500 if you have someone do it for you. I wanted to keep a Porsche engine in my 914 but the cost to build one to over 300 hp and then rebuild if it broke was too much for me to bear. For the power I wanted and the budget I had in mind I could have went with the V8 option. But I also wanted something a little different than what had already been done so I chose the 3 rotor 20b.
If you are looking for reliabilty go for a normally aspirated engine. If you are looking for more than 300 hp from a 13b turbocharging is the only way but be prepared to learn what has to be done to get that kind of power reliably out of a rotary engine.
