Hi Caro,
First of all, you should not consider **ANY METRIC **as a ranking factor. This said, generically speaking, there is no guaratee that a page/domain that has a higher PA/DA/TF/CF or whatever metric, will rank better than other with lower scores.
Those metrics try to simulate what googles consider as authority and measure how likely is that page to get higher rankings.
Secondly, you should stick with one version, the best that you and your marketing niche consider is the best (could be www or non-www or even a subdomain). Then just setting the 301 redirection corretly you will not have any SEO issue, and eventually those metrics will be passed to the selected version.
In the case that you dont have the R301 set up correctly (or it isnt possible) you can use canonicals as well.
Thirdly, In my experience, google does not like changing frequently the prefered version of a web. I'd advise you to stick with it now, for some reason you've moved it anyway.
To citate the same resource as the question es nearly the same:
There is also a great post from Cyrus Sheperd, stating that redirects do pass authority correctly:
301 Redirects Rules Change: What You Need to Know for SEO - Moz Blog
Hope it helps.
Best luck
GR