Since you're looking specifically for the pros and cons of turbine single SIC time, I'll offer what I experienced (I flew for a turbine single operator and sat right seat until I met 135 minimums, all per their Ops Specs):

Pros: flying in all conditions (day, night, icing, thunderstorms, blizzards, etc) to all sorts of different airports, all in the system and all before having to do it on your own. CRM, turbine, 135 (read: commercial) experience. Overall fantastic experience and confidence builder, much more so than flying the same hour 500x instructing.

Cons: some employers will be skeptical, as many operators fly aircraft with a right seater (mostly for insurance reasons) that don't require a right seater (Caravans, PC-12s, Navajos, Twin Cessnas, King Airs, some Citations, etc). So do your homework and MAKE SURE (as in read for yourself, not take their word for it) there are provisions for SICs in their Ops Specs. Turbine single operations which require an SIC include no/inop autopilot and flying more than 8 hours on a trip. Another con is many operators who offer turbine single SIC positions also have a contract. Avoid contracts if at all possible. Oh, and the pay typically is about poverty level.