He seems to be saying that if you quit your job, then you will have a better chance at getting another job during a time period of a bad economy than someone that got laid off. I don't find that to be true. I never have.
Leaving a job voluntarily has looked better historically to future employers than being laid off, for the simple reason that there is always the question about why
you were laid off - and when future employers call for references there is very little information that can legally be given. I don't know if the current market is taking RIFs as negatively as they have in the past (you were downsized, but why was your
job downsized instead of somebody else's?)
But by all means finding the other job first and then giving appropriate notice shows more responsibility than quitting.