In the case of advantages of having a single companies product, the financial ones are that I would assume there would be some sort of a discount for exclusivity from the airline. While I havent seen it in print, I would be very surprised if airbus, or boeing doesnt make it worth an airlines while to use only their product. This is pretty standard in all business, so I would be surprised if it didnt happen here.
You mentioned commonality, this is a major factor. In the case of Continental for example. They want to get the fleet down to 5 types of aircraft. This reduces costs for training, for parts, for mechanics, for just about everything really. If they only have Boeing 737, 757, 767, 777 and MD80 which I think will follow the DC-10'S out the door in the next few years
As far as a company like United using both the A319 and the 737 and the reasons for it, some factors could be
Mergers, United is a product of various mergers, and it could be that along the way they aquired either as assets. I could also be just using all thats available to them. Without getting into a who's better, Airbus and Boeing have better planes than each other for different reasons
Just my guesses