Tags are a big part of Delicious. In addition to discovering featured content on Delicious, you can also view the recently saved links and search for links via tags. You can check a user's profile to view their top tags, saved links and organized stacks. StumbleUpon is more free-flow and kind of random, based on interests and pages you've liked. Once you've started stumbling, the StumbleUpon toolbar appears along the top of the page if you don't have the toolbar installed. This toolbar allows you to switch to a new page by clicking the "Stumble" button. You can further refine your interests by clicking the like button, and remove certain items and niche interests by using the dislike button.
All StumbleUpon functions take place from a toolbar, either added to the page or as an extension for your browser. Also, webmasters can add a StumbleUpon button to their website. You can also add StumbleUpon to your iOS or Android device. Tools for Delicious allow you to add a link to your profile without leaving the page but do not offer search functions. One such tool is the Delicious bookmarklet, a small bit of code you add as a bookmark to your browser's bookmark bar and click when you want to add an item to Delicious. You can also download Delicious extensions for Firefox, Chrome and Internet Explorer. Delicious also offers a button for your website.
Pages marked as "liked" on StumbleUpon are saved to your profile as your favorites. Other users can view and even stumble through your favorites. Although you can view your favorites at stumbleupon.com/favorites, it's not as rigidly organized as Delicious. In contrast, Delicious is perfect for storing and organizing your favorite links.
In conclusion; I think I would personally prefer Delicious as an organization tool but StumbleUpon for when I am just surfing and not looking to do anything planned or organized which is not often but there are those times when I am just in a curious mood and want to check out the rest of the world.