Pro's of a welded diff: Cheap. Almost as fast as a fancy diff IF the car is set up right. You'll never lock up just one rear tire...
Con's: Properly set up cars for a welded rear end will wear tires faster; they will be scary to drive over the range of high speed and low speed corners; if the welds fail, it's bad; if it's not set up right, you will get lots of understeer (as in hello wall); impossible to roll the car around in the paddock, driveway, garage etc.
For a road coarse, a car with a welded diff needs to be set up like a go-kart--that is it MUST lift the inside rear wheel when going around corners. This is typically done with significant rear anti-sway bar. Suspension springs must then be selected that will result in a somewhat balanced car when it's on 3 wheels. A roll cage structure that really stiffens the chassis will help tremendously. It will eat rear tires (because only one is on the ground while going around corners). Good damping will also help. If you are not afraid of oversteer, it can be fast. Note that extra care is required in esses and chicanes--the car will require more time to transition from one direction to the other than a car with all 4 wheels on the ground (the suspension physically moves more and transfers more weight around in a welded diff car).
FWIW, many many moons ago I got to play with a formula SAE car that could run either a Torsen or a spool. Properly set up, the spool was as fast as the torsen around an auto-cross type track. Around a faster track, it had too much oversteer with a spool. Very comfortable with the Torsen though.
Hope that helps,
Tak
#29 ITA SFR SCCA