Some of the differences:
AMD uses on-cpu memory controller (as I read on MaximumPC mag., this
contributes to the overall better performance).
AMD (Athlon64 and all other -64 families) support 64-bit datawidth
capability. AMD is the first set the 64-bit standard (AMD64, or X86_64 as
in GCC), while Intel follows it.
AMD is also the first in x86 world to implement dual-core, and will be the
first to release quad-core.
Based on many benchmarks performed by diverse testers, AMD outperforms
Intel's Pentium4 in many applications, especially the ones w/ rich
floating-point computations.
Not sure about temperature, because I have also Pentium-m based laptop,
and it is cool, even cooler than AMD64 3400 laptop (that I also have).
But I think is more something to not-good-design issue from Compaq (I have
Compaq Presario R3000z based on AMD64 3400+. Lowest clock: 800 MHz, max
clock: 2.2 GHz). My other laptop is IBM T42p
with Pentium-m processor (lowest clock: 600 MHz, max clock: 2.1 GHz).
The bottomline is, if you want to get overall performance or 64-bit, go
for AMD. If power is more important, I think Pentium-m is slightly
better.