Positive displacement displacement blowers make almost constant boost. This means you're getting more boost in the lower RPM range. They make more heat, and it's not as easy to set up an intercooler.
Centrifugal blowers make boost proportional to the square of the RPM, so the boost has to build similar to a turbo. They're more thermally efficient and make less heat. As for transmission problems:
Originally Posted by Procharger
Superchargers can be used with automatic or manual transmissions and will not increase transmission wear under normal driving. When racing, however, the additional torque provided by supercharging will place additional load on the transmission, especially when increased traction is present, such as with slicks. This impact is minimized when the boost increases with engine rpm, as is the case with centrifugal supercharging and turbocharging.