I like belt-drives, but I notice that BMW seems to be abandoning them. Currently their only model with a belt-drive is the F800ST. At one time they also had a belt drive on the 650cc Scarver and the F800S. They have moved to (or retained) chain-drive for the G650GS, the F650/800GS and the new F800R models. The rest of their bikes have shaft-drive, which are nice - provided they don't break, which they occasionally do. The shaft drive on my 1991 K100RS snapped at 46K miles and wiped out my entire swing arm assembly and everything inside. The new parts cost $1200 and that was with 1996 money.
My favorite rear drive for a street motorcycle is either a belt or a fully-enclosed chain drive running in an oil bath. However, dirt bikes need to stick with a chain drive due to the environment that they ride in.
On the other hand, an open chain drive is probably the least expensive to make and design and allows the easiest gearing changes.