AR-15: Lighter, dirtier, needs to be cleaned more often, bad for a lefty comp to Mini, cheaper and crappier magazines
Mini-14: Heavier, cleaner running, will run dry, easier for a lefty, better magazines, newer ones are just as accurate as an AR at the same price point
The thing with ARs is you can't go cheap, and they don't do well for swamp/woods hunting and requires more cleaning. The 30 round magazines and up also tend to malfunction due to poor magazine design, most you can only fit 28 rounds, lest the first few have issues. The gun is also subject to jamming easier with increased friction (i.e. if it is not lubed or very dirty) :
http://www.youtube.com/watch?v=6JmIQXkoog8