I wouldn't rate Best's fallout at all as it came from a man who was truly sick (alcohol is an illness). I happen to know people who were there during one of Best's binge drinking and the description of it was that it was sad and that the man had no control over himself. You can't really judge someone who doesn't have control over himself.
The worst 4 fallouts we had were Teveth, Keane's, Ronaldo's and Rooney's. I think that the least serious was Tevez. It was evident that United didn't considered him as a first teamer anymore which meant that he was on the way out either way. Teveth should have left with some class but you can't ask that from a player that lacks such thing.
Keane comes next. It wasn't really public (MUTV isn't exactly outside United's domain) and in my opinion, it was down to Keane's frustration over United's (ffs we were playing Smith as a CM) and his own decline. Keane's career went up in flames after that which shows how ill thought that interview was.
Rooney's criticism was more serious then Keane's as it was done with independent media, at a time when he was still useful and with a plan in mind (ie Mou wanted him at Chelsea). However similar to Keane, Rooney's spat was in reaction to United's decline. Which leads us to the worst of all ie Ronaldo's. This fraud speaks as if he is a United legend when he left us prior to his prime, he joined us at a time when no one wanted him and he was quite happy to do so even though he knew that the club was in difficulty. The only reason why he kicked the hornet's nest was because he wasn't the centre of attention anymore and everything around that interview (the timing + the interviewer) was made to cause as much damage as possible.