Whether and open diff or a limited slip diff will break the rear end loose in a corner and slide sooner is one of those "it depends" questions.
With an open diff the inside rear wheel will break loose first and the amount of lateral grip provided by the wheel drops significantly. If the outside rear wheel is not at its lateral traction limit, it will most likely be able to handle the additional lateral grip that the inside rear wheel was providing. If it does slide it will start in a more gradual manner but is more difficult to control. In that case, no rear slide. But, there's an added rear grip loss caused by weight transfer forward because acceleration is reduced. This might be enough to induce a slide.
With a LSD you don't have the inside wheel traction loss problem so ultimate lateral grip under acceleration is higher. But, depending on the LSD (and more so with a spool or welded diff) once the accelerative traction limit is reached, breakaway is quicker then with an open diff, but more controllable.
So, to summarize, the LSD will have higher lateral traction limit under acceleration then an open diff but will breakaway in a more abrupt manner (depending on the style of the diff). Once sliding it is very controllable with the throttle. The open diff will have a lower lateral traction limit under acceleration then a LSD and will break away in a more gradual manner, but be less controllable once things start sliding. Throttle changes will not affect the slide very much.