I just really don't like the Eccleston dude. I've never seen his Dr. Who, but I don't like him in anything else.
I thought he was brilliant in Shallow Grave. His character wasn't all that likable, but then again, all of the characters were pretty much jerks. You felt sorry and repulsed by all of them at different stages.
I recently saw him in eXistenZ, though his character was a bit of a bore (which was admitted in the story as well, which was interesting).
He's an interesting Doctor, though he is not as whimsical as Tenant and Smith. He's cavalier about what's happening, but he also has a bit of a callous side to him.
I would say that Tenant and Smith are more fun.
I'm not familiar with the previous Doctors, though I have Netflix now and could remedy that.
And yet really, you have to view him for who the character is at that point in the story. He's just come (or recently enough, anyway) from the Time War. He's very scarred, and very rough still. He's lost a lot of the life and whimsical nature that is often associated with The Doctor. He just went through a transformation of sorts (different than Regeneration), and he's not yet healed from the things that he did in the name of... Justice? Righteousness? Self-Reward? Anger?... Who knows. (Hopefully all of us quite soon!)
It's what makes the story of Rose so poignant. The Doctor so often saves humanity, but here she is, saving him. This is very well written in the story of "Dalek", when Rose puts herself between the Dalek and the Doctor, begging the Doctor not to harm the Dalek. The Doctor's war crazed anger and fury releases as he demands Rose move so that he can destroy this thing that has caused so much damage throughout the universe - this thing that is a danger to the very existence of reality, and Rose responds "He's not the one pointing a gun at me".
Yes, Eccleston lacks the whimsy and compassion and overall likability that Smith or Tenant bring. But for who he is emotionally, I think he's quite perfect for the role.