I don't think you'll see much of a performance increase from an P4 3.2 to an X2 3800+. Even multi-threaded apps and general multi-tasking won't "trounce" the P4, as someone above claimed.
You can find benchmarks comparing the P4 540 (a later edition of the P4 3.2GHz) and a modern X2 3800+ Windsor
here. As you can see, even with multitasking you're only looking at a 40-50% performance increase; in single-threaded apps the gain slips to 20-40%. This is definitely an improvement, but I don't think it justifies a new rig. If that's all the speed you need, consider overclocking the P4 (if your motherboard permits) and/or adding more memory. If you have a dual-core capable board, you might consider popping in a used Pentium D 925 (probably ~$80 in the fs/t forum). If your board is both dual-core capable and overclockable, you can get a Pentium D 805 for ~$50 and crank it up to 925 speed (or better).
But if you're moving to a new platform, that means a considerable amount of money, which means you'll want to make sure you get more than a 20-50% performance increase. Try this configuration:
$117 Microsoft Windows Vista Home Premium 32-bit OEM
$115 Intel Core 2 Duo E4300 retail
$85 Gigabyte GA-945P-S3 LGA775 motherboard
$80 Seagate Barracuda 7200.10 320GB SATA/300 hard disk
$65 Raidmax Apex ATX-802BP mid-tower case w/450W PSU
$50 Wintec AMPO 1GB (2x512MB) DDR2-800 memory
$49 Biostar V7102GL13 7100GS passive video card
$44 FSP Group ATX400-PA power supply
$33 Lite-on LH-20A1P-186 DVD burner retail
$12 Samsung SFD321B/LBL1 floppy drive
It comes out to $640-$650, depending on how shipping is consolidated. Then you can part out and sell the P4 system, maybe getting $150-$200 back.