Yes, cottage cheese is a complete protein.
Is any protein better than another protein? My understanding is that it depends upon what you are trying to accomplish.
In general, whey protein is probably more quickly absorbed than cottage cheese. So, it may be better for post workout nutrition. There is a broad range of types of whey protein. The isolates are very quickly absorbed. Some whey products may be combined with multiple forms of whey and other proteins such as caseine to provide fast, medium, and slow absorbtion.
Wheys can offer convenience also.
Cottage cheese is an excellent source of protein and contain caseine so you get some slower absorbing protein that is good for regular consumption and pre-sleed use.
I don't use any one protein to the exclusion of another. Use a variety of sources and combine them. Cottage cheese with a good flavored whey powder and a little water makes a great pudding like snack. Throw in some fruit and/or nuts to gain some good carbs and fat.