My two cents:
having flown HEMS in mountains/onshore and Oil&Gas as well with Aw139, B412 and BK117, I can tell operational wise they're both effective for an array of reasons.
Skids are more durable as wheels do get consumed by use, wheels get flat, in mountain the tripod landing gear gives more stability on rough terrain, in swampy landings you may want skids instead of wheels, wheeled landing gear is more prone to failures to retract or extend (ECL issues to be addressed with proper training during OPC's and LPC's), on snow doesn't really matter because both systems use removable snow skids (mandatory on all Hems winter contracts), on drill ships you may want wheels because the net is often installed on the decks and skids get entangled, having to haul in and out airports wheels are better as you can taxi without hovering for the time taken to commercial aircrafts to clear the taxiways with heavy departing traffic, the belly is usually higher on skids helicopter so antennas and drain pipes are more protected from intercepting the ground....
Cheers