What has been mentioned here in this thread seems to playing into our world at work as well. Our intranet (which we currently use DNN for) has gone through a few phases over the years starting with a dirty home-grown app (before my time). They moved from that to a 3rd party one called EAS, then moved from that to one called Passageways (they moved to this one just before I started). Between the high cost and poor support and extensibility of Passageways, I bided my time until I felt that I had enough clout to start suggesting alternatives. So, we went down that path again. We evaluated possibly building our own or using a multitude of options out there. I had just come from a job where we used WSS1.0 to spawn off a few sites for some clients and so I had a very bitter taste in my mouth for Sharepoint, so I didn't even consider it an option.
Long story short we settled on DNN because of the vast community, relative extensibility in skinning and programming, and the cost -- free framework, inexpensive modules, fairly easy to develop modules for. We have been using DNN in production since May of 2007 though we started our development and testing phase in October or November of 2006. It has been a great move for us and we service rougly 15000 requests per day; our portal contains approximately 600 tabs, 60+ security roles (which is how we handle "department" sites -- we create a base page that has the rights to create/edit and then anybody with security to that page can spawn children pages and modules to them).
However... the powers that be have recently started stirring the pot and we are now going to start evaluating MOSS for our intranet. We belong to a Microsoft volume licensing package and already pay out the bum for it and since MOSS is included in our license, they want to actually use it. As I type this they are setting up some servers in VM for me to create a test site on and start evaluating it against our needs.
One thing that I've seen on the thread here and definitely agree with is that DNN == internet presence; MOSS == intranet presence. While either can be used for intranet or internet, it seems that you get the most power and functionality out of MOSS with its Office integration and very tight (and good) integration with AD. DotNetNuke has AD integration (I haven't looked at the new stuff, so my opinion here is based on older stuff) but I think it is mediocre at best. Office integration exists only when/if somebody writes a module to do it, but frankly anything out there pales in comparison to Microsoft integrating with their own stuff.
With ASP.NET 2.0, Sharepoint became a heck of a lot easier to develop and skin. They used to say that you couldn't reskin a WSS1.0 site... I've learned that you can but it was a pain in the bum. I'd provide examples here of sites I DID reskin in WSS1.0 but the company I worked for no longer exists and, as such, the sites have been migrated from WSS and are hosted elsewhere (so the point is moot). Anyway, masterpages were an excellent introduction into ASP.NET 2.0 and Sharepoint leverages that technology wonderfully. Web parts in WSS1.0/1.1 were crap. They were such a pain to do ANYTHING with so we ended up cheating and using a third party component which allowed us to host ASCX in a web part (I believe it was called smarttools or something like that), much like DNN. However, since Sharepoint was rebuilt from the ground up with WSS2 to support ASP.NET 2.0, their whole model actually works now. You can create your Web Parts in Visual Studio a heck of a lot easier now and the CAS isn't such a crap.
On the flipside, DNN's way of deploying modules is 100x better than Sharepoint is. Zip up my package and upload it, voila! Sharepoint is a bit trickier but by virtue of that trickery it is also much more secure. Lets face it, anybody can create a module for DNN and provide it for free and drive traffic to it, but then have it one massive trojan. The code is there and very easy to pull all sorts of information out of DNN using a module, then easily email it somewhere or do whatever you want with it. Scary? Sharepoint webparts are rarely free and typically have some pretty big players supporting them, so it is easy to trust them when installing them.
DNN modules are typically less than $200, though about 90% of them out there are crap. Sharepoint web parts are rarely less than $500 but they are very well developed and well supported, just a lot less to choose from.
A HUGE selling point for DNN is the community. Sharepoint has a community but (this is based on my experience with WSS1) it is not very responsive or helpful. The DNN community will generally answer your questions if they are well-formulated and well-placed, not to mention the sheer size of it. Is it well organized? No, but it is getting there.
DNN support -- if you want to pay for it you get it from the source or from other trusted members of the community (such as Mitchel Sellers). Microsoft support -- you get to call, wait in line, and then talk to somebody in India that you struggle to understand what the heck they are saying for half the call, then the other half the call trying to get them to understand what you are saying and prove that the problem you are describing really does exist and is well documented on the internet, you are just trying to get them to help you resolve it, end up getting escalated to somebody that natively speaks English (somebody out of Redmond finally), and they solve your problem in 5 minutes (true story, not with Sharepoint though).
Hopefully that gives you a little bit of insight into each side of the story.