Hi Kris,
Yes PA will increase with a naked domain - Google has outlined that it enjoys seeing this and has directions on how to do it with Google Sites (Link Below):
https://support.google.com/a/answer/2518373?hl=en
Redirecting is a good move and can be done through your CMS - how you do this will depend on what you are using to operate your site. Keep in mind that redirects can affect the power of any links pointing to your Home Page and this will affect link juice flowing through the rest of your site to some degree. Depending on the scope of your service area and what kind of SEO you are running (Local, Global or PPC), this will have a greater or lesser impact on what you do moving forward.
In terms of what is creating the better PA - a combination of Google's approach to ranking sites and what your external links are pointing to are probably the answer. If external links are pointing to your naked domain instead of the www. version, this would explain what you are seeing.
Without knowing the site or the context it's hard to know for sure, but those are my guesses.
Hope this helps and fire any additional questions/info you want at me and I will try to help out as best I can.
Cheers,
Rob