Oh, Toën is using a different definition of "localization" than the one I am accustomed to (e.g., see Definition 5.2.7.2 and Warning 5.2.7.3 of Higher Topos Theory). Since Cat is a presentable category, I assumed you were taking the localization in presentable categories, which involves a category S-1Cat and an adjunction with left adjoint Cat → S-1Cat which has the analogous universal property with respect to adjunctions between presentable categories. In that case, S-1Cat turns out to be rigid categories and Chris explained why you might expect this to be true. (The homotopy category of Cat is presumably not a presentable category at all.)
With S the class of equivalences of categories these localizations do not agree because S is not closed under pushouts in Cat: in the square
J -> BZ* -> *the left-hand map is in S but the right-hand map is not and yet the square is, bizarrely, a pushout. (What makes things even trickier is the ∞-categorical analogue of "S is closed under pushouts" is true because of course we must take homotopy pushouts. In short thinking of Cat as a 1-category and trying to work with equivalences there can lead to strange results!)
