In regards to external services (Dribbble, Behance, and Deviant) what is the purpose of having a portfolio website but you link all your images externally and take a viewer away from the main site and purpose?
From a user experience perspective it doesn't make sense to do this. Generally users wouldn't appreciate a link to a site that has the same content.
I can think of cases where it would make sense, however. An employer or possible client could view it as you being very engaged in the graphic design community. Showing you are active at other sites conveys your passionate about your craft. Even if a user doesn't click those image links it immediately conveys this through recognition.
Secondly, if these sites were used to show other things in your portfolio, like a design process or contribution to another project, I think it would be beneficial as well. One of the really cool things I've come to learn about Behance is that designers will sometimes show the steps that were involved in creating a design. It demonstrates their expertise.
There is a final reason that isn't a good reason, but I am pretty sure is the main reason for this choice. Other graphic designers are doing it. Brands engage in similar ways with social media. They don't do it because they have determined the efficacy of external links to be great, they are simply followers who feel they will be left behind if they don't. Following the crowd, however, has never been the best way to distinguish yourself.
My theory on why.... ease. Many people don't know how to, or don't want to, build an image gallery themselves. And, in many cases, some may not even know enough to download and set up a gallery package. After all, managing data can be a job unto itself if you want to edit it frequently.
As to pitfalls, for a general portfolio site I don't think it really matters. If you send an employer to Behance, et. al, they don't really care as long as the site functions. They are looking at the work, not the web app in most cases. Of course it depends on the position requirements - obviously you wouldn't be applying for a web development job and want to send an employer to something you didn't personally build. But if you're a print-focused designer or an illustrator using an external service to display your pieces is not necessarily a bad thing. I've used a gallery site or two and gotten random jobs out of the blue because someone happened to be browsing and saw my illustrations.
If you are a freelancer or small business, then external services don't reflect that well upon you at times. If you rely on other products for your own work, potential clients will assume you rely on them for their work. That is of course, unless the external service is brand-free or invisible on the front end.
If you are trying to get business, it's not the best idea.
The only good reason I can think of is that by having your images on a really public site like Deviant, you will probably get more exposure. More people will see your stuff through searches,related, etc.
But beyond that it's not the best plan. Ideally you should have your portfolio on your own personal site. But if you're not looking for business then who cares where they are.
The other problem is that if you send people away to look at your portfolio on a site like Behance or Deviant they may just find someone better than you.