There’s no such thing as an older language.
Similarly, there is no such thing as an older dialect. Sure, for example, the English of England has been spoken in the same place for 1500 years. But the English of America retains a bunch of features that have died out in the English of England; the subjunctive, for instance, or faucet, or gotten.
So what is your metric for archaism? Linguists usually aren’t bothered much, for languages or dialects, so they just make the occasional impressionistic judgement, mostly based on phonological conservatism.
If you’re going to be more rigorous about it, you formulate as rules the major phonological shifts from the common ancestor to each of the two dialects, and you count the rules up; and you do the same with morphological shifts, syntactic shifts, and lexicon (somehow—believe me, there’s a lot more to count). But noone bothers to: the impressionistic judgement is good enough most of the time.
The one time someone did go to the bother of counting up all the phonological shifts from Middle Chinese to Cantonese and Mandarin respectively, and modelling them as two different state machines, http://www.aclweb.org/anthology/…, they came up with the conclusion that Cantonese is phonologically more archaic than Mandarin. Mandarin has half the tones and none of the final oral stops of Cantonese; I could have told you that impressionistically, based on those two factors alone.