Do you need the brute force of a P4 in there or would a more efficient, power saving processor like a Centrino Pentium M do you just as well?
A 1.8Ghz Centrino is about a 2.8ghz P4 and a 2.0 Ghz Centrino is about a 3.2ghz P4. I think thats a fair assessment.
The Centrino's really do very very well with battery life, compared to the P4 laptops. If you will be pluggin into the wall 90% of the time though, it probably doesn't matter what you get, just as long as it can handle whatever apps you throw at it and you get it for a good price.
What kind of price can you get the Z81G for, and what do you plan to use it for? I don't many ppl have them here.