The debate of what's the best Bug Out Gun, an M14 or an AR15 is ongoing and will never be resolved. Two schools of thought, each having their Pros and Cons. People tend to forget that the roll out of the M14 had just as many issues as the roll out of the M16 (most of which were due to the Military's Ordinance Department screw ups). The issues with both were addressed and resolved for the most part, but the fact that there were issues in the first place has influenced opinions.
Personally, the underlying problem with one's Bug Out gear will be weight in my opinion. To me,, Bugging Out means getting the Hell out of Dodge as quickly as possible. It's not a leisurely stroll through the toolies, but a concerted effort to get to a more secure and defendable location as quickly and safely as possible, therefore, the weight of one's gear is a critical factor. Too much weight will slow your progress, and that could prove deadly very quickly. One will need a rifle and enough ammunition for planned needs and unanticipated problems, and 7.62 X 51 NATO is considerably heavier than 5.56 X 45 NATO, thus it stands to reason one can't carry as much of the former versus the latter. Same goes for the rifles themselves. The M14, even polymer stocked is still heavier than an AR. For individuals with smaller stature, lugging an M14 over hill and Dale will be burdensome.
Others will tout the virtues of the M14. In the end one must make an informed choice, and be honest with themselves about their capabilities and limitations. The answer of which gun is better for their Bug Out, depends upon one's honest analysis of one's strengths and handicaps.