There isn't any of the spirit of the old characters. Abrams' characters are two-dimensional, thinly-veiled caricatures of the original crew, at best. McCoy does nothing of value, ever, and every time Karl Urban utters a one-liner it is painfully evident the scriptwriters are trying to make him a grouchy old man without ever having watched Kelly DeForest. Kirk is an idiot with no redeeming features and who should be in a mental institution because his sociopathic idiocy makes him a danger to everyone else around him. Unlike the original who even at his worst wasn't completely brainless. Spock, always the most interesting of the original crew, completely lacks the subtlety and nuance of Leonard Nimoy's, as if the writers simply decided that making him speak awkwardly was enough to give him depth (and judging from the posts on this forum, most people appear to mistake that for actual characterization). The rest of the characters are all the same.
It's difficult to tell whether the actors are genuinely awful and incapable, or whether they are simply doing the best they can with shitty scriptwriting and directing. I lean towards the latter, personally.