I think Carter has been active because he honestly wants to make the world a better place not just to toot his own horn like Obama.
i mean, i think obama honestly wants to make the world a better place too, but yeah carters more altruistic. still, the tradition of going away is more the gentleman's thing to do, its not a long tradition that has suddenly been broken.
Most of the former presidents already had long careers serving the country in some capacity before becoming president so it makes sense that they would retire from the limelight, so to speak. Taft was probably the biggest exception since he went on to become Supreme Court Chief Justice.
Yep, Carter is a decent human being. His work through the years with Habitat for Humanity has been impressive. Has Obama ever picked up a hammer and help build a home for a homeless person? Nope. Will he ever? Nope.
https://en.wikipedia.org/wiki/Jimmy_Carter