There's an older thread over at the David Allen Co Forum that discusses this very topic.

If you want my take on EverNote (I use both, but tend to blog about EN more, since I use it every day, all day), you can take a look at my posts on EN. See here.

For an actual answer for you: The two programs have two different paradigms. Think of ON as a multi-subject notebook with coloured tabs. You can organize stuff in notebooks, sections, folders, pages, sub-pages. You can flip through pages, like you would with a meat-space notebook. Think of EN as a huge roll of paper, where you keep adding stuff to the bottom (everything is time-stamped). The beauty of EN is not the paradigm of endless tape though - it's the ability to categorize the individual notes in the tape. You can have an entire hierarchy of categories, even copies/shortcuts of categories (you won't realize how useful that is until you try it!). Automatic categorization of notes based on content, but more useful, based on keywords. The ability to choose multiple categories to get OR, and the ability to look at category intersection to get AND between your categories. And the search is amazingly fast.

For me, I use EN every day. Where should I paste that confirmation that my membership has been renewed? EN. Where should I organize all of my project support material? EN. Where should I make a list of books that I want to read? EN. So, what do I use ON for then? Well, there are some things in my references files that I just don't want to have to scroll through (long notes in EN are scrolled, and it's not that great looking). Sometimes I just want to flip through stuff, and I don't need it to be automatically categorized, or sorted by time created. Examples are recipes, crochet patterns, really cool images that I've found online and want to look at again sometime in the future but don't need to look for, etc.

I basically think of ON as a set of scrapbooks that I organize by topic. When I want to look at recipes, I can browse ON. EN, on the other hand, is my primary source for research notes, miscellaneous stuff that might come up again, project support material (including keeping lists of NAs), etc. etc.