In the grand scheme of things, 3 months pay is not that significant (a large enough performance bonus can already match that, or a joining bonus for that matter). Now compare that against the chances that you will enjoy your new same-pay job less, or you'll have to move far away, or delay career advancement while you learn the ropes at the new job. There are plenty of potential advantages from changing jobs too, depending on the job, so it actually might make a lot of sense to switch. The point here is that 3 months of salary tips the balance only slightly.
Of course, those who have reservations about working where they are, should take the severance package, but that's the point.
Also, I am a bit surprised that we are discussing 3 months of pay as a magnanimous, almost foolish, concession from management, whereas in many places around the world that kind of compensation is law mandated when you lay-off people without reason.