Let's compare. At the 2016 national conventions...
The Democrats will have:
1. Barack Obama, an outgoing president who is very popular with his own party.
2. Bill Clinton, a former president who is very popular with his party and with a number of non-Democrats.
3. Jimmy Carter, a former president who was rather mediocre but is somewhat well-regarded as a humanitarian/elder statesman figure.
The Republicans will have:
1. George W. Bush, a former president who is unpopular with much of his party and with most non-Republicans, to the point that he was not welcome at the 2008 and 2012 conventions and probably won't attend the 2016 convention either.
2. George H. W. Bush, a former president whose ideology is so divorced from the modern GOP that it's hard to see him feeling welcome to play an active role in the party without some sort of time machine. And even if he wanted to, he's too feeble and unhealthy at this point to be involved.
Pretty sure the Republicans win on this count, since Democrats have Carter. Without him, your point would be much stronger.
Very few people take particular pride or great joy in Carter's record as president, but he's really not
reviled any more except by you.
Poll
