Tennant did a good job in the role, he certainly cared about the character having been a fan since he was a kid. Unfortunately as RTD started to go batshit crazy that effected Tennant's portrayal since he had inferior scripts and production.
Eccleston to me was just a guy who didn't give a shit about Doctor Who and picked up the role as a laugh. He had the shortest (voluntary) tenure and never really had enough to time to make the role his own.

Bow ties are coool.