I do not know why the First Order and/or the New Republic chose not to use clones in their armies, but I have a theory as to why Disney and the creative team did.
In reality, when it comes to any decision that Disney makes with respect to its film universes, be it animated, Marvel, or Star Wars, the simple answer is: money. Disney realized that it could catch more flies with honey than with vinegar (not that you should try to catch flies with vinegar).
Kennedy, Abrams, Kasdan et. al. wanted to wash the bad taste of the prequels out of our mouths and have us remember the good feelings we had for the original trilogy. For that reason many things established in the prequels are simply ignored, removed or never mentioned - and we thank them for that (midichlorians, anyone?). And they went to the expanded universe for "inspiration" only. This approach kills two birds with one stone - it appeases the die-hard fans of the Prequels, an lures the disgruntled fans back to a galaxy far, far away. Maintaining and expanding the fan base is crucial to their financial success. I believe this is a key reason behind all the story decisions that were made in The Force Awakens.
In the star wars universe (Films Only), the new storm troopers are not only recruits, but it is also implied that they are better than clones. The clones from the original trilogy have a (unwarranted) reputation for being incompetent (OK, there was that incident where they lost the battle of Endor to some teddy bears...).
Establishing the new storm troopers as "not-clones" they instantly become more of of a threat within the star wars universe - its no longer easy to defeat them. This improves the tone of the film. Every "disposal" trooper is now a valid adversary to the heroes.