It might be possible to parallel the two different brands depending on the parallel kit wire connections. There is something about that on the Champion web site, so ask them about your proposed combo.
No, you cannot just add the watts even with the same brand and the same size. It goes with the lower watt one what the parallel kit receptacle can pass along. (also there is the actual running watts, not what the gen is named at)
With two the same watts, you get less than the total out--it is false to say (as they advertise) that you "double" what you can get with one.
EG, Briggs and Stratton says in their manual for the P2200 (I have that one):
P2200 + P2200 = 3,000w output
P2200 + P3000 = 3,000w output
P3000 + P3000 = 4,800w output
So it must be due to the parallel kit itself that is used. Champion does say using a big gen with a little gen is possible but not "optimum". Perhaps that is like with the 2200 + 3000 above, where you have to go with the lower one.