McCartney is a different type of album. First, let's talk about that title. This is a name that had been paired with Lennon, separated by a slash, for years-- we weren't used to seeing it all by itself. When the media ran stories on McCartney, he was often just "Paul." He could have called his album Paul McCartney, but he pointedly did not. I think he wanted people to see his name out there as a songwriting credit, without the old prefix. And the album he made has some parallels to Lennon's, too. They share a rawness, a seeming desire to move away from the opulence of 1969's Abbey Road, the last album the Beatles recorded together. But where the rawness of Plastic Ono Band plays into anger, aggression, and disillusionment, the rawness of McCartney is only in the sound. The record has a homespun charm, and a feel that suggests McCartney wasn't putting too much pressure on himself to carry on the Beatles flame or make a statement.
From The Onion's A.V. Club:
The sense that McCartney might’ve had two classics on par with his Beatles best had he worked just a little harder on McCartney and McCartney II sometimes makes listening to the reissues feel like retracing lost opportunities. But for the most part, what comes through is McCartney’s remarkable ability to create catchy hooks seemingly off the top of his head, as well as his playful sense of experimentation and lack of rock-star pretensions.