The Dothan is an optimized die shrink of Banias, in a nutshell. With same cache, Dothan and Banias should be almost identical in performance. In RL Dothan beats Banias because they have double cache.
You considering a Celeron M notebook? The chip almost performs as well as the Pentium M, with one thing missing. IIRC it doesn't have advanced speedstep, so battery life won't be as good as Pentium M, though it should be much better than Celeron/P4, and still a bit better than mobile Celeron/P4, relatively speaking.