I'm currently on season 3 but I have agree so far Eccleston stood out more as an alien entity who is more peeved yet curious to be around humans where Tennent has is a very giddy child hoping around space and time.
I agree with you guys as well regarding Eccleston. He definitely gave off more of the tough pissed off persona that is suiting to an intimidating alien. But I think that is due a lot to the fact that he was written as the bitter and lonely Doctor. Rose's character was put in place to kind of break him out of that, which is why Tennant's doctor tended to be a lot looser and less bitter towards everything. Rose broke down the wall the time war had built up within him.
We kind of see Smith portray that bitter Doctor again during the season 7 Christmas special after he loses Amy and Rory.
As a side note, after creating this thread I decided to go back and check out some of the classic Doctors again, and I would definitely have to say that Troughton is my second favorite after Tennant.