The La Sals and Abajos can have monsoon rains, usually mid July through September and are somewhat similar to the San Juans or the Mogollon Rim, but the monsoon isn't quite as strong.
The Uintas have thunderstorms in July through early September and are similar weather wise to the Colorado mountains.
The Southern Wasatch can have thunderstorms, but not nearly to the extent of the Colorado ranges, the Mogollon Rim or the Uinta Mountains. Although they do happen occasionally, thunderstorms are rare enough in the Wasatch that the afternoons are probably the most popular time of the day to be on top of a peak.
Although the Southern Wasatch (or the rest of the Wasatch for that matter) have much less thunderstorms than the Uintas or the Colorado ranges, they typically get a lot more snow and are much wetter in the winter. Unlike much of Colorado, Arizona and much of Southern Utah, summer is by far the driest season in the Wasatch. See the below weather chart for Alta, for example:http://www.wrcc.dri.edu/cgi-bin/cliMAIN.pl?utalta