Depends on what you want to use it for. If you are only interested in email, browsing the internet, and word processing then the celeron is probably ok. If you want to do ANY gaming at all, don't get a celeron. Personally I would never buy a celeron, but that is just me. In my opinion, the Pentium-M is the best processor for a laptop.

Celerons are ok for running office, internet and e-mail as mentioned but when it comes to running lots of programs at once, gaming, video/photo editing and doing any processor intensive tasks it slows down majorly. My friends new Toshiba with a 2.4ghz Celeron feels like it runs slower than my pentium III on my old I3800. But thats my opinion.

It probably does run slower than your PIII, the newer celerons are terrible processors. A duron (AMD) 1.6ghz has been shown to beat a celeron 2.6 in almost everything. The celeron "D" series is better, but still not very good. For a value notebook, I'd recommend an AMD Athlon XP-M processor. For anything else, I'd reccomend the Pentium M, which is in my opinion the only good thing to come out of intel in the past couple years.