When the Cheyenne's first came out the Cheyenne II was actually the first model. There were some perceived pitch stability problems that related to pitch feedback inasmuch that the pitch forces did not correspond to what was considered "normal" for that class of aircraft. If I remember correctly there were a number of crashes that was attributed to this situation.
To remedy this condition Piper installed a "Stability Augmentation System" referred to as "SAS". The SAS system consists of a spring, bobweights, actuator,SAS vane and computer that would vary the elevator load for airspeed and angle of attack. An operative SAS is a go/no go item.
This system is pretty typical in larger part 25 aircraft and was not usually seen in part 23 aircraft , so it created some consternation. Piper then created the Cheyenne I, which had less powerful engines. I do not remember the rating but 580 eshp seems to come to mind. The installation of these engines negated the requirement for SAS, so this was accomplished to salvage the marketing disaster of the original Cheyenne.
The Cheyenne II has PT6-27's which are rated at 620 eshp and this represents a fair amount more power. You might want to check with an insurance company to see what kind of differences in rates there are for the Cheyenne I vs the II.
On a side note: I have flown the II in rather adverse conditions, specifically ferrying the aircraft overseas (tanks, overweight, etc.) It was a bit squirrely in those conditions, when operated normally it seemed fine. It was also rumored that there were a number of pilots that would operate with the SAS system either inop, or deactivated. The important note here is that you would have to operate the aircraft with strict adherence to airspeed readings as your pitch feedback will not correspond to what you would experience in other aircraft operated under the same conditions.
Have fun!