In the information tab of the "Wordpress" tag in StackOverflow you can read:
WordPress Answers Stack Exchange
An evolving Stack Exchange site dedicated to WordPress. WordPress questions not about programming are best asked here.
This quote means that, if I have a WordPress question which is related to programming, I will probably ask it on SO. I expect SO users to be programming savvy, so they will probably answer my question faster or help me understand my problems better. However, if my Wordpress question is not programming related, I will of course use WPSE.
Since my original post, some things have changed both in StackOverflow and in my opinion.
First, as you can see in the comments below, the description of the Wordpress tag in StackOverflow as been changed, and I believe it makes more sense, leaving no room for misinterpretation.
Also, after asking the same question (which was quite urgent) in both this website and StackOverflow, I can tell that it had much more attention in here (specially after I created a bounty, of course). Since the question was 100% about programming (Wordpress related), I can honestly say that this website is more active than StackOverflow regarding this issue. In two days, in this website I had about 60 views. The same question in StackOverflow had about 25 views.
I guess that, as people are becoming (as JCVD would put it) aware of this website, they are starting to use it more for Wordpress related issues. From now one, I will definitelly come to Wordpress@StackExchante first, and only then go to StackOverflow if I have the need to. For this, I just have to thank the StackExchange Wordpress community and be a part of it as a proud member.