Conceptually, JavaScript cannot be compared to ASP. JavaScript is a language, ASP is a technology. (I guess some could argue that a language is a technology.) You can use JavsScript in ASP. It all really depends on what you want to do. If you are looking into building dynamic (scripted) web sites, you will need some kind of server-side HTML generation technology: ASP; ASP.Net; Cold Fusion; PHP; Perl; etc etc. Do you want to stay with a particular OS? That would affect your choice. Do you want to go with open source technology? If you already have a host where your HTML lives, what at the capabilities of that host?
I would recommend learning ASP.net as it's the latest in the MS family of server-side web technologies and is very powerful. Depending on your knowledge, you may need to start with a beginning book to learn the basics of programming techique.
I'd start with one of these (depending on which language you'd like to learn):
Beginning ASP.NET 1.0 with C#
Beginning ASP.NET 1.0 with VB.NET
Peter
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Work smarter, not harder.