Personally, I just like Mini-14's better than standard AR15's. You can make either platform super accurate. Although it will take sending your Mini-14 to Accuracy Systems to do so, as opposed to marrying an accurized barreled upper to an AR15 lower.
I own an AR15 and an AC556 (full-auto version of the mini-14). There are just some things I like better about the Mini-14 - rugged and dependable. My AR15 shows signs of wear just getting gently banged sitting in my safe. Ever see what an AR15 looks like after 10's of thousands of rounds and serious use? They can get pretty crappy looking. After all, they are just aluminum.
My AC556 is blued steel. It generally doesn't get scratched and I can use cold blue to touch up any place that the blue has worn a little. It's easy to clean and doesn't need to be cleaned 1/2 as often as my AR15 does. There are some nice stocks out there for the Mini-14 as well - both wooden and tactical. I happen to have a SCAR CQB folder on it right now which makes it more tactical.
Also, I've always liked the all stainless versions of the Mini-14. Personally, I like the shinier stainless on the older Mini/s - I'd look for one of those and have ASI put a true target barrel on it and mount it in a nice laminate stock. Something like that just does it for me over the AR15 - dime-a-dozen tacticool rigs.