Your question is unanswerable. You've first got to define what you need your computer for and how you're going to use it. Secondly, you obviously have checked out limited sales vendors. The 1.86ghz system has half of the better features, whereas the 1.73 ghz system is better in the other features. You can go to vendors that have ALL of the features you want.
First, if you need to hook up to a network at work, you need XP Pro. Period.
Second, if you do serious graphics work, you need the 15" screen. In fact you need to spend $100 extra for the "Flexview wide viewing angle" screen.
Third, if you do a lot of traveling, especially air travel, you need the smaller 14.1" screen.
Fourth, for most common office applications and internet browsing, the lesser 1.73 ghz processor is sufficient. Heavy database and professional graphics applications require a faster processor .... perhaps a 2 ghz. In fact, the heavy-duty applications require more memory (which could easily be added later) than 512 mb.
I'm guessing, based on your question phrasing, that a lighter-duty processor and 512 mb ram will be sufficient. Your answer will probably boil down to (1) the more portable 14" screen vs the better for graphics applications 15" screen and (2) whether you need to hook up to networks. Please do yourself a favor and analyze your needs.