What page does Google find most important?

Maybe you all have an opinion on this. (unfortunately I won't be providing actual URLs here)

I've been optimizing a couple of pages for specific keywords. When I do "keyword phrase site:www.siteName.com" the page I've been optimizing comes up first. This leads me to believe that THIS is the page that Google deems to be most important for that search phrase.

However, when I do the same search out in the wild, a completely different page appears. I've tried this same search from different browsers and logged-in/not logged-in to my Google account. This unwanted page always seems to appear.

Do I chalk this up to some kind of personalization? Any thoughts? Once again, I apologize for not having specific URLs here.