I don't know much about Ron Dayne, but I can tell you about William Green. The problem with Green is a severe lack of instincts. Green is a fairly powerful, fast runner with a lot of physical ability, but he has very little instinctual or mental ability. He does not have the vision to find holes quickly, let alone anticipate their opening. Even when he does find a hole (which, granted, are few and far between in Cleveland) he does not exhibit the burst needed in the NFL to take advantage of it. So, typically what you see from him is that the QB hands the ball off to him and he kind of hesistates and waits, and either runs into his blockers or the defense. Most of his runs are negative yard or 1-2 yard gains. Every now and then he'll bust off a big run, but only when the hole is gaping and he has time to get up to speed.
When given time and space, Green has enough athletic ability to show something. That's why he was a special teams standout on the Browns. He could get down the field pretty quick and make some athletic stops. It if wasn't for his special teams play he would've been kicked off the squad as soon as Romeo got here. That, coupled with his youth and potential for development is what kept him around for so long. He was also a very hard worker (which Romeo remarked on a few times) so that probably helped too.
The off the field issues were a problem, but it is generally regarded that he's cleaned up but is still not good enough to start in the NFL.