I run 10w30 in Kohlers with the hydraulic valve lifters. They seem to run quietest on 10w30. I've tried Rotella T6 5w40, and Rotella T5 10w30, and I'm currently running Pennzoil Platinum in mine. After this change I will switch back to the Kohler 10w30 though. Their oil for whatever reason seems to run best in these Command V-Twins. I'm not one that usually buys an equipment manufacturer's own brand (I don't like the Briggs oil, way over priced) but the Kohler oil I found works best.
As far as a 5w30 versus a 10w30 I think it has to do with shear. These engines run pretty hot. 250* oil temps are normal, and some of the landscaping guys report 290* temps even with oil coolers.