As it happens, for San Diego specifically, METAREA and MET2013 are directly comparable because the San Diego metro area (labeled as “San Diego-Carlsbad” in the 2013 definition) has always covered the same geographic extent throughout its history, and both METAREA and MET2013 are able to identify that extent exactly.
I determined this first by looking at the list of counties defining metro areas for METAREA, which Matthew shared. To determine which counties are associated with the 2013 metro areas, I found the 2013 list on this Census Bureau page. In all of these sources, the San Diego (+ Carlsbad) metro area corresponds exactly to San Diego County.
Next, I also checked this listing of incompletely identified metro areas for METAREA, and I checked the omission and commission errors for MET2013 through the links at the bottom of the MET2013 variable description. There have been no mismatch errors for this metro area for either METAREA or MET2013.
So, in this case, METAREA and MET2013 are complete and exactly comparable (as long as you take account of the different numeric code they each use to identify San Diego). For other metro areas, they often aren’t comparable, so Matthew’s general advice is true for many other use cases!