Let the war begin!! Both the Intellites and AMDers will likely have their say, so I'll try to be as objective as I can, and rely what I've learned (some of which may be flawed):
Pentium M (Dothan core)
The Pentium-M Dothan core uses a 90 nm production which reduces both the die size, and the power consumption. I believe they only use around 18-24 W, which gives around a 5 hour battery life on a standard 8 cell, Lithium Ion battery. They also have about a 1.5-1.6 multiplier for performance comparision to Pentium 4 laptops (so a 1.8 GHz Pentium-M would compare to about a 2.7~2.9 GHz Pentium 4. All in all, this is one of the best processors Intel ever made, led only slightly by the Pentium Pro (in my opinion, of course).
Athlon 64 DTR
An extremely hot burning chip at 81.5 W of average consumption, this makes for a very poor portable chip. Of course, it's meant for DeskTop Replacement laptops, so they really shouldn't be used for extremely mobile laptops. You'll usually get around 1-2 hours of battery life, depending how heavily you tax the system. The good side to this processor, however, is that it is usually a cut above the Dothan's in performance, usually better by about 15-20% at the same frequency. Of course, the Athlon 64 has support for 64 bit computing, and also outperforms equally match Pentium 4 systems, usually with ease.
Mobile Athlon 64
Everything about the DTR chip holds true for the Mobile Athlon 64, except power consumption (only down to 62 W), battery life (1.5-3 hours), and the performance increase over the Dothan (about 10-15%).
Low Power Mobile Athlon 64
Short of being a mouthful to say, the LP Athlon 64 is a very nice improvement over the Mobile and DTR chips, burning a scant 35 W. It's a bit higher than the Pentium-Ms, but for Athlon 64 standards, that's probably as good as it's going to get. It performs better than the Dothan, but not by too much (I'd say between 5-10% at equal frequency). The low power usages increase the battery life to around 3-4 hours, though the Acer Ferrari users claim they only get around 2-3 hours of normal use (probably due to the hotter burning Radeon 9700 chip).
Well, I hope most of this is right, and doesn't spawn a war. I've tried to hold back my love of AMD chips, and provide a fair analysis. It really comes down to what you have to have. If performance is key, you can't beat the Athlon 64 for performance and price. If battery life is a must, the Pentium-M Dothan core is a much better hope for you.