If you mean private tour vs Crruise Ship tour, be VERY sure about access to the island. From what I read on forums, ONLY the (pricey) ship tours will transport you via special boat to the bigger modern port, & transfer you to a bus up the road to the clifftop surface of the island. Otherwise, a pvt. tour may meet you AT the clifftop... which means you need to wait with all the other 2,000 or so passengers for space in the "tenders" that take you to the Old Pier at the foot of hte cliffs, then wait in line for the very-limited capacity cable car to llift you to the top... this could take a loooong time. And the return could take even longer. On a busy weekday, when many cruise ships are in port, the cable-car line has reportedly been over an hour. Of course, in late September there may be fewer ships,. There are websites that can tell you richt now just how many cruise ships will be docking the same day as yours.
Before you get until details of tour length, find out about access!