You're comparing apples to oranges here. Yes, everything you listed is an Intel x86 part, but the Z3735F is the CPU in my Windows 8 tablet, which has a 4W "SDP" (scenario design power).
The P8400 has a TDP of 25W, or about 6 times the heat dissipation of the Z series atom. So of course the Core 2 can beat an Atom, it's in a completely different category of processor.
If you are going to compare apples to apples, pick the i5 2410M. It's not a new part, but the TDP is comparable to the P8400, and the target market (12.5-15" laptops) is the same.
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i5-2410M+...
Here you can see that the newer laptop-class CPUs out perform the Core 2 by a factor of 2. Couple this with much better integrated graphics, and newer memory (4GB DDR2 SODIMMs exist but compatibility is spotty and they're quite expensive) and it's not really a contest anymore, the newer CPU/chipset provide better performance and will give you longer battery life.
I am not going to claim I am one of those people who needs a powerful processor in my laptop, because 90% of what I do is login to remote servers who do the work much faster than my laptop ever could. But, I do enjoy getting 5-8 hours of battery life thanks to my newer processor sipping electrons when idle, which cannot be said for Core 2 era systems.