Republican Presidents make better former Presidents than Democrat ones. They do not behave as if they are still in the White House as the last two Democrat ones have been doing -particularly Carter. Republican Presidents don't criticize the sitting President even if from the other party in this country, much less go to a foreign country and do it. Personally I never wanted to see or hear from Carter again in my lifetime and consider him an arrogant asshole, anti-semitic puffbag full of himself trotting around as if some kind of great statesman. As if the entire world was constantly CLAMORING for him on behalf of all people everywhere as their only savior. He was absolutely THE worst President in my lifetime with no one even a close second. He always overestimated his intelligence and capabilities when in office and just can't help but continue doing so until he is dead no doubt. No matter who is in office, he believes he is the guy everyone would really prefer to be President at all times. He was and is no statesman of any kind and has only created more problems for the country by sticking his nose where no President wanted him or invited him. He does it whether the current President is a Republican or Democrat, so Obama had better be prepared to have this guy trying to insert himself into the picture one way or another. Arrogant little prick was an embarrassment to the country when he was in office, he continues to be an embarrassment to the country and a thorn in the side of every single President since he got booted out of office. He should have stuck with building houses for Habitat for Humanity and just accepted the fact Americans already told him what they really thought of him when they overwhelmingly decided to boot him out of office.
Clinton's biggest fear about leaving office has come true -he can't command the spotlight the same way anymore, he isn't considered such a fascinating guy or political personality on the scene and he isn't the one crowds are adoring. But even he hasn't stuck his nose into events where he was never invited like Carter does -although they both seem to think shooting their mouths off and criticizing the current President here and abroad is part of their "job".
Bush will do what his father did after leaving office. Go live his life as a private citizen, enjoy leaving the stress behind and eventually write his Presidential memoirs. But he will not criticize Obama while he's in office or ever give his opinion on issues Obama is dealing with. When he gives any interviews in the future, he will be willing to discuss issues HE had to deal with -but not how he thinks the guy who has the job should be handling things. But he will undoubtedly enjoy not being the constant target of those who suffer from Bush Derangement Syndrome since they will either have to focus their insanity on someone else or end up institutionalized.
I think it was Thomas Jefferson who said that although former Presidents often believe otherwise, they serve no useful purpose to our system -and they should either be forced to emigrate to another country or executed. If he had to deal with Carter as a former President - he might not have meant it as a joke though.