Neither of them passed the character test, l think. My thoughts on Miliband has already been stated, but Burnham seemed to have concluded that because he made a mess of the leadership election that it would be the only chance he'd ever get and so went off to Manchester when the opportunity presented itself. If he had carried on with what he had been doing (Shadow HS), he'd probably have been Shadow HS instead of Abbott in 2017 and the result might have been better than it was (and if it didn't, he'd have been in a much better position to be the next leader).
If I had to pick someone from the centre or right now as the next leader, I would pick Starmer who actually has engaged with the membership, engaged with the leadership, worked at developing policy and changing it where necessary and basically done what decent politicians should do. He turned up to a recent fundraiser at our CLP (though I didn't go) and was by all accounts a really nice bloke.
He still would be absolutely monstered by the media, though. That is what we should all remember.