An unfair comparison at the moment. Shaw will soon be in his seventh season at Utd, Williams is in his first with the first team. A better comparison would be, is Williams at 19 as good as Shaw was when he came to Utd age 19, and can he be as good as him in the near future?
Shaw came with a glowing reputation from Southampton, but remember that LVG, when he first arrived at Utd, stated "Luke Shaw is not fit" and put him on a fitness regime. From there on until his leg break in Oct 15 he had a good run of form, but when Mourinho arrived, his fitness was being questioned again. Even allowing for Mourinho's habit of publicly undermining players with calculated malevolence, when two managers question a player's commitment there is probably some truth in the suggestion.
Ole's handling of Shaw has almost certainly improved Shaw's form where Mourinho's regular humiliations damaged his form, but it's clear that Shaw is a player that has needed to be pushed and that the competition from Williams this season has provided that. The good news is that he has hit that streak of good form while still only 24, so he has some good years ahead of him if he can adapt mentally to the reality that his physique means he needs to put in a particular effort to stay fit. That, of course, could be bad news for Williams.
Williams has rougher edges at the same age as Shaw was when he arrived at Utd, but he can take great credit from the way he has slotted into the first team pretty seamlessly. He is tenacious, intense, quick and forward-thinking. His tackling and passing need to improve and his judgment is probably not as good as Shaw's was at the same age. He should be judged, though, on his own merits - neither favoured because he's an academy product, nor discarded because previous academy players (James, CBJ, Blackett, etc) haven't made it.
So, at present, Shaw is a more rounded player and ahead of Williams as first-choice LB, but I believe Williams will improve with experience and has a bright future given the chance. On an admittedly complete biased note, it's good to have two Mancunians in the first team as well.