I agree with most of the comments here. These are two great destinations for different reasons. Two days is enough to see Muscat; to explore the country beyond that you'd need a few more days.

I would recommend 2 days in Oman, focusing on Muscat, and the rest in Lebanon. (Maybe another day or two if you want to relax by the pool or beach at one of the resorts, which are nicer than any in Beirut.) Muscat has a few sites, especially the Muttrah souk and nearby forts. Thought it has virtually no good dining or nightlife; Beirut has tons.

I would recommend Umm Sherif and Babel as two spectacular modern Lebanese restaurants in Beirut. (Babel is sort of outside town.)