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.
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Core2+Duo+P840...
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Atom+Z3735F+%4...
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Atom+C2338+%40...
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Atom+E3845+%40...
(Look at the single-thread rating and you'll see that a single Core 2 core is 2-3x faster than a single Atom core.)
Unless you're doing something particularly CPU-intensive, which doesn't tend to be the use-case for a 12.1" ultralight laptop, that processor is more than enough. The small screen resolution may get a bit annoying though.