In most benchmarks the XP 2000+ is just about neck and neck with the 2.0 GHz Northwood P4. Individual programs will vary though. Those useing SSE2 will definately run faster on the P4 - and those without often run faster on the XP. However you are comparing it to the 1.8 GHz Northwood. On average, at stock speed you should expect the XP 2000+ to be roughly 10% faster than the 1.8 GHz Northwood - which probably won't be noticible.
As for pricing, the lowest priced XP 2000+ costs $127 and the lowest priced 1.8 GHz Northwood costs $155. So yes there is a price difference. However, the stock P4 runs great while the XP generally runs best with a new heatsink/fan. When you add that cost in, the prices are about the same. I suppose you could buy the 1.8 GHz Williamette to save a few bucks, but the performance just isn't the same.
If you overclock each to the max, the 1.8 will be faster unless you got a really unlucky chip that doesn't overclock much.
In conclusion for the same price, you could get roughly a 10% faster computer if you go AMD at stock speed.