When I search for similar questions that I am going to ask, I usually can't find anything through search box in stackoverflow. But when I enter my question in "Ask Question" page, the questions suggested through the "Questions with similar titles" box are usually relevant. Do you experience the same thing?
I used to think the same thing (and even thought of posting this very question at some point), but after thinking about it for a while, I came to the conclusion that something different probably was the reason:
When I use the search box, I type in some keywords, some things that might have to do with what I'm looking for.
When I use the question title box, I actually type in a question, so I really think about how to phrase this thing as a question.
I believe that this is actually the reason for the (perceived) better results: You phrase your search differently.
Bear in mind that Ask searches on title ONLY. Nothing else is looked at: body, tags, nothing. It's a pure title match.
Edit: there is now an advanced search operator, "title:1" which you can see here
The search box has many more features than the Ask Question title box. You can see the options here.. Also the search box strips away common words and keeps keywords. But outside of that they should be searching the same things.
Make sure when you're searching in the search box to use it like the ask question box. But remember that it is stripping away non keywords. You can even see what words it's stripping out.
Here I'm asking the question "When are the dev days happening?
When you click that and then click any tab (like relevance or newest). Then check out what the search query is consisted of. In this case it's changed to "dev days happening"