I've done the same on two different projects.
From my experience it should be fairly straight forward to update your webforms and normal usage of the Sitecore API. There might be minor changes, but it shouldn't take too long.
All of your hookins into pipelines etc. might still compile. But you will want to check if it's still needed. It may be a fixed bug, or some functionality that has been added to the main product (such as language fallback).
Even if it's functionality that's still needed, and does compile, you will want to check if it's still placed the correct place, there are lots of new pipelines and processors.
By far the hardest part of the upgrade is analytics (from DMS to XDB). If you're not using DMS, you're in luck :)
As for migrating the Sitecore CMS data, I had problems with the database upgrade scripts on my first project, and ended up moving the data with a combination of Unicorn (for templates and settings) and Sitecore Sidekick for the content data (or Razl, if you prefer the paid alternative).