I have a dual PIII 1gig and my mother-in-law has a P4 1.5. In Photoshop and Premier, she takes me to the cleaners. I narrow the gap when I put the 256 megs of ram back in that I removed to level the playing field, but she still has an edge. My dual machine shines when I load it down with SQL, Visio, Outlook and Word simultaneously - it's a workhorse. I guess it's like comparing a throughrobred to a clydesdale.
You also may want to consider the fact that the PIII is an older generation being replaced by the P4. Adobe's relationship with Intel means that their Windows-based apps will soon be optimized for the P4.
I'd say go with the P4 and as much ram as you can afford.
(I hear the plethora of recommendations for better hard drives and video cards coming)