My P4 is the newer (relative) model Prescott based 90nm HT. The dual core Atom would win because of optimisations in core logic and newer instruction sets, not to mention it can handle 4 threads, instead of 2. What's more insulting is that ATOM CPU's are in-order execution processors, and P4's are out-of-order, which should make the P4's a lot more efficient, but sadly, it's not enough.
The P4's netburst architecture was designed for high clock speed processing, so it had high latencies. Intel quickly found out they couldn't produce the 5GHz+ chips that they wanted within a sane TDP. Adventurous overclockers managed to get the chips to 7GHz+ i believe, but under EXTREME conditions.
All in all, P4's are a long lasting workhorse that's ridiculously inefficient by modern standards. Even when it comes to recycling, you'd save money in the long run buy BUYING an ATOM, since the P4 consumes a lot more power, thus bump up the bill by a fair margin.
maybe 3 or 4 times. And, last I tested it, 'egg's return system is totally online & easy to use. That is assuming you access to another computer to access! 
