The Police as well weren't much of friends, but all were great musicians in their own right and you could hear it in their music.
The impression I get though with John and Paul is kind of like what family members, brothers, go through over the death of a parent. A lot of issues arise out of how money, property, arrangments are handled and obviously people are going to disagree. This would likely have been the motivation of both of them "attacking" each other in the early 70's after "The Beatles/Apple" died. Inside, I'm sure they always considered themselves as close as any brother, and I believe (I'm not 100% sure about this) that they only started to speak to each other after 1976 when most of the legal problems were over.