Is paying down debt the equivalent of savings?
IMO, no.
Not exactly, but it does have the effect of increasing your net worth (everything else being equal).
Some advisors say that paying off debt is the same as investing your money and earning whatever the interest rate on the debt is.
Regardless of all the punditry, paying down debt is a good thing, IMHO. "Snowballing" is an effective way to do it, too.