According to an entry for the word usage in a Japanese dictionary:
http://dictionary.goo.ne.jp/leaf/jn2/134173/m0u/
you could in principle use 「大の」 a bit more liberally to put a larger emphasis on something.
I agree that the usage of 「大の」 seems to be somewhat limited to a certain set of words like 好物, 親友, 仲良し, or idiomatic cases like
大の大人がいつまでもアニメなんて観てるんじゃないの
(Roughly translates to "an adult at your age should not be watching anime any more.")
You can also find cases where the usage might not be so prevalent yet still seems natural, such as 大のおしどり夫婦 and 大のスポーツファン (both of which to me sound okay). But in other cases they just sound awkward to my ears, like 大の先輩、大の女優, etc. Although if it were put this way:
あなたみたいな大の女優がマリファナなんて吸ってるんじゃないの。せめてコカインにしなさい。
(An actress of your stature should not be smoking weed. Go for crack at least.) then it actually does sound natural to me, likely because this case follows the idiomatic pattern that I quoted above for 大の大人. So, if you dig deeper, there might be a way to understand a rule or two about why one sounds okay but others feel awkward, but asking グーグル先生 didn't yield anything useful for me to understand this better.
Do you think it depends on which word/phrase is more common?-- Ah, it might be.Is 大の親友 used equally as much as 大親友?-- I would say 大の親友 is used more than 大親友 but this is my opinion so you should hear how others think. – Teno Oct 3 '12 at 5:06