The dual-core is worlds faster than the p4.
A dual-core is a single chip with two cores stuck inside. These cores are much more advanced than a P4 core, they have shorter pipelines, Higher IPC rate (instructions per clock), A better all-around architecture. This is what makes it better, it's like comparing a Blunt club to a Rapier.
But you can't just add the two cores together.. Some applications will not benefit from a dual-core. The programs themselves have to be compatible with the chip, they have to be multi-threaded to allow both processor cores to work on a single application. Multi-threaded apps, as well as multi-tasking itself will benefit by a dual-core however.
Realize that most apps will benefit from a dual-core in the very near future, And that multi-core chips are nothing, if not the future.