The primary advantage of synthetic base motor oil is longer life due to the base stock's greater resistance to oxidation from time exposure to operating temperatures. Most OEMs who specify synthetic nowadays include an oil quality monitoring system that includes a sensor that measures the oil's dielectric strength, which is a primary measurment of oil quality. Oil is an insulator, but as it breaks down and becomes contaminated from engine operation its resistance decreases.
Without an oil monitoring system it's tough to know how much longer you can go between changes, but at three times the price you need to go two to three times longer between changes to make it economically efficient.
Beyond the longer life due to lower oxidation resistance, synthetics don't have any other significant advantages. They are not "more slippery", nor do they have a better additive package than any other API SL rated oil. They do have a couple of other advantages that are not applicable in too many cases, such as a lower pour point for better flow at arctic winter temperatures, and their higher oxidation resistance makes them a good candidate for applications that run excessive oil temps - like consistently over 250 degrees F.
Early blends have a reputation for causing older polymer seals to leak, but supposedly this has been corrected on current blends.
Bottom line IMO is to stick with conventional oil and follow Jeep's recommended change intervals - time or mileage, whichever occurs first.