With a capsulorraphy, the implant is replaced into the pre-existing pocket. The front wall of the pocket is sewn to the back wall along the plane you wish the implant to sit.
With a neosubpectoral pocket, a new pocket is dissected in front of the front wall of the capsule around the implant, stopping where you want the new inframammary fold to be. Since a portion of this dissection is behind the muscle and is a new space, it is called "neo subpectoral" or "neo retropectoral."
Both achieve the same goal. One has not been shown to be better than the other. The only thing that matters for you is that you find a surgeon very experienced at fixing your problem. Depending upon the extent of your problem and condition of your tissues, a good repair is usually possible.
I am increasingly using the neosubpectoral approach for a variety of reasons: it is faster, easier, more accurate, less painful, and looks better sooner. But if the tissue is very thin and incapable of supporting sutures and the weight of the implant, I will often reinforce the bottom of the pocket with acellular dermal matrix such as Strattice.
One thing you need to know; if your doctor tells you that you need to go smaller, heed his or her advice. Big implants with thin skin can decrease your chances of a longlasting successful repair.
By the way I think you are misusing the term "bottoming out;" the methods you have referenced are used to treat "inferior implant malposition." Bottoming out is a stretch deformity of the lower pole of the breast in which the distance between the nipple and the inframammary fold increases. The treatment for it is a breast lift. Many surgeons and patients confuse these terms.