Late to the discussion but I've always loved the Ruger Mini's. They aren't the most accurate rifles, nor the fastest to reload, or even the most customizeable, but they have their own strengths that are worth consideration.
Accuracy: Definitely the first thing that gets mentioned when we talk about the Mini 14. The pencil profile barrels of the early models are prone to barrel whip and the groups open up further after shooting a few rounds. That said, post 2005 models are more accurate due to a slightly heavier barrel, and the recent "Tactical" models with an even thicker barrel and threaded muzzles will go toe to toe with a cheap stock AR. Like most other things in life, accuracy can be improved by throwing money at the problem. Accu-struts and muzzle weight reduce barrel harmonics and tighten groups. Cryo treatment adds no weight and will improve groups and reduce accuracy degradation from a hot barrel. Target models and aftermarket bull barrels from Accuracy Systems Inc can be had for a small fortune.
Straight-stock designs such as the Mini offer their own inherent advantages and disadvantages. For some a straight stock is faster and more natural to point and operate than a pistol gripped rifle though an AR with a collapsing telestock has more adjustability for different sized shooters. The Mini's straight stock design is more compatible with narrow storage spaces. It has a shorter vertical profile, a consideration for storage and caching. An AR measures about 9" top to bottom at the widest points with standard sights. The Mini measures about 5". The Mini's straight stock design allows for lower sight and scope height over the barrel. In practical application this lets the rifleman use his cover more effectively. His head doesn't protrude as high above the barrel when firing from behind cover, presenting less of a target. When shooting through a peephole, a smaller hole can be utilized. The flip side of this (pun intended) is more muzzle rise during recoil than an AR due to the higher bore axis. The Mini's design is compatible with folding stocks to reduce front to back overall length. The AR has a folding stock option but is cost prohibitive and renders the rifle unusable until deployed. I'm not a fan of bullpup stocks but that option is available for the Mini if that's your bag.
Aesthetics: They bear strong resemblance to the M1 Garand, M1A, and M1 Carbine. In my own subjective opinion an iron and wood stocked rifle has more character than an all black AR, and looks less threatening than an AR or AK. If used in self defense it's not as scary to a jury as an evil black bullet hose.
Takedown: The Mini has less serviceable parts to lose and is easy to take down. Pull open the trigger guard and the rifle practically disassembles itself. Care must be taken when scrubbing the bore as you can only insert a cleaning rod through the muzzle. If using a sectioned cleaning rod use a bore guide to preserve the barrel crown.
Lightweight: Depending on the configuration, generally at least a pound or two less than most stock AR's though exceptions exist.
Durability: I've broke an AR charging handle trying to extract a stuck case. The Mini's steel operating rod/slide assembly is stronger than the AR's thin aluminum charging handle. The Mini's extractor is wider and beefier so it's less prone to breakage and less likely to shear the rim off a sticking case. Unfortunately Ruger has not yet learned the benefits of nitriding or chrome lining so barrel life will be shorter than that of a lined AR barrel.
Operating system: The Mini uses piston operation rather than direct gas impingement. Put rudely, the Mini doesnt sh*t where it eats like an AR so it's easier to keep the receiver clean and the operator won't get sprayed with hot gasses in the face. It's also less sensitive to over or under lubrication and the generous tolerances of the open receiver are less likely to gum up with sand and debris that might find its way in than an AR. The Mini's bolt is out in the open and easy to view without tilting the rifle 90 degrees to peek into a narrow ejection port so checking to see if a cartridge is in the chamber is easier both visually and by touch in the dark. The operating handle reciprocates, so care must be taken to keep fingers and objects out of its way when firing, but pushing a stubborn bolt into battery is easier with this type of charging design than the forward assist afterthought on an AR.
Magazine changes: Generally slower than an AR but can be sped up with custom parts and training.
Magazine availability: Factory mags are best, aftermarket mags are problematic for the most part though I've had good luck with Thermold and Tapco magazines, as well as Beta-C and MWG drums
Optics: Though iron sight options are limited and difficult to adjust, the Ranch and post 2005 Mini models are easy to scope. Ultimak makes a picatinny scout rail that replaces the upper handguard and works great for forward optic fans.
Sorry for the long winded post, I hope this gives any potential buyers some things to consider before dismissing the Mini.