The new version is very similar to 1.x, but they've made vast improvements to the web architecture, controls, functionality, security, productivity of the IDE, and performance of the classes.
If you're starting learning from scratch, there's very little reason not to learn the new stuff.
Highlights of the new features include (but are not limited to):
**Master Pages**
Have a modifiable template for the pages of your site to easily manage and cascade changes (or programmatically change it to provide a customized view for users).
**Skinned Controls/ Themes**
Like CSS for server control properties. Helps make a site's look-and-feel easily manageable and flexible.
**Provider Models For Membership, Viewstate, Etc.**
If you don't like Microsoft's implementation of a certain feature, you can just change it and swap out your component for theirs! This comes in really handy with membership especially.
**Security Controls**
You have a set of controls to login, logout, apply for membership, display the number of users online, edit your user account information, etc. The best part? With the functionality provided with the MembershipProvider, these UI components require literally NO CODING to make them work. You just drag them onto the form.
**Data Controls**
With the new data objects, you can also potentially have, say, a grid that requires absolutely no coding. Usually you'll end up doing a little coding for these controls, though.
**Performance Gains**
Reflection is faster, DataAdapters now do batch updates, DataSets can be serialized into binary format for fast transport (though I don't like DataSets), etc.
**Language Features**
Generics, anonymous methods, nullable types, woo hoo! I had a custom collection that was 500 lines of generated code, and with generics we trimmed it down to literally one line!
**API Improvements**
TryCast(), String.IsNullOrEmpty(), Page.ClientScript... Booya!
Anyway, the new stuff is definitely the way to go.