(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.
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.
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.
I know there are more powerful CPUs available; the point is whether that CPU is sufficient for most of the things you're likely to use this laptop for. Is your Win8 tablet too slow, or does it do what you want with good performance?
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.