If you're going to upgrade the Pentium 4 without swapping the board, my recommendation would be a Northwood core based - these are a larger process node, have less cache, and top out at lower frequencies.... but intel screwed the pooch in moving to the Prescott architecture, so they're also slightly better performance per clock (even with less cache) and significantly more power efficient. Also prevents any worries about power draw from the motherboard or the power supply LeCroy picked.
I've upgraded a couple of these scopes without swapping the motherboard and my usual is: 2.8GHz Northwood P4, 4GB RAM (XP/2000 can't use all of it anyways), and a PATA/IDE SSD DoM with an image of the original drive. That's all flat upgrades from base configuration, but requires no driver changes, configuration options, or fan/heatsink replacement and the whole thing with a 32GB DoM can be done for less than $60. Also going with a disk on module means you can get rid of the IDE cable, you don't have to worry about mounting holes (PATA SSDs are usually 2.5" format, so you need new holes if you want to mount it where the HDD is normally), and you make the whole unit slightly lighter and slightly less airflow obstructed.
I believe the Windows 2000 based machines have an earlier revision intel board that will still support up to like 3.06GHz CPUs but no more, whereas the windows XP machines come with the slightly newer motherboard with extended CPU support, including hyperthreading, but the same socket (and still no dual core).