Let's put aside the mechanics of how the different "forum" software works for the moment. I think StackOverflow has a big advantage there, but obviously access to someone who can actually answer your question will trump that.
In this case, there is a perception that the vendor forums are more likely to be able to answer your question. That perception may or may not be accurate. There might be a more established community with original developers for the product watching the vendor forum, or StackOverflow may have a few brilliant gurus on that topic and others who don't yet stand out due to lack of questions.
This perception is an important consideration. You want to ask your question such that you have the best chance of finding an answer. Keeping that in mind, you're probably going to search google before you post. And StackOverflow generally does an excellent job getting it's content into google, so there's a good chance that over time you'll find yourself coming to StackOverflow anyway, as problems are solved one question at a time. I've seen questions asked on StackOverflow that reference a failed google search, and less than three hours after the question is asked not only is there a well-voted accepted answer on StackOverflow, but the question is now the top result for the Google search.
Additionally, you want to consider the larger issue of making help for your topic more widely available. While you might get a better answer to this question from a vendor forum, long term you have something to gain by pushing to move all questions on your topic to a place where the result is more likely to be indexed by google. Not only will your initial google search be more likely over time to solve the problem, but as this also solves problems for others earlier in the process it will free up the gurus who answer questions for your topic to deal with more new questions rather than re-answering the same question over and over, which will help increase the available archived knowledge.