Propane has roughly 25% less energy per gallon than gasoline, even E10 gas, so a lot more is consumed to produce X watts of power. How that effects the economics depends on the priced of propane/LPG vs E10 gasoline in your area. Propane prices vary widely, both by the sales source and the type of purchase (portable bottles vs bulk delivery(. If you run a portable genset on portable LP bottles, you will often be paying top dollar for the propane. Buying 20# exchange bottles at a Blue Rhino outlet, for example, typically costs about $5.75/gallon. Many propane refillers charge $3.00-$3.99 per gallon, but others may be substantially less. Bulk delivery may well be down around $2.00/gal. to refull a large fixed tank.
Do the arithmetic for regular E10 gas vs propane in your area, but I'm betting the gasoline is the winner in most cases. The advantage of propane is the convenience and safety of the enclosed tanks rather than cost of operation.