I have both,and like both. But I think too many points are in favor of the AR to go with the mini-14.
If the Ruger was still a fraction of the cost of the AR, I'd likely suggest that route, but they're not.
Ruger mags are expensive and less common than AR mags. They also don't load into the rifle as instantly or intuitively.
The AR comes in several more varieties, barrel lengths and is more accessorizable.
There are also many manufacturers with varying degrees of quality. You can go "budget AR" and still have a decent rifle ( $699 S&W at CDNN ) or go as nice and high-end as you care to (Colt,Bravo,Noeveske,LMT, etc.)
The AR's are more accurate,even over the newer,improved 580 series.
Also, an AR is going to have substantially better re-sale potential,always an important consideration.
Almost forgot, assembly and disassembly of the AR is considerably less of a PITA than that bolt and recoil spring on the Mini.
As suggested above,take her to a gunstore and have her shoulder both rifles, she'll tell you real quick which she likes better. :thumb: