If you (1) feel that you can effectively address the weaknesses of your application until next cycle (- and doing well in methods/research design classes at Columbia will certainly add to the quality of your application), (2) have a strong preference for working at a top 15-20 university after finishing your PhD, and (3) can afford the MA at Columbia, I could see why you are considering to turn down Cornell in order to get into a better program in the future .
There is an undeniable difference in placements between, for instance, Harvard/Stanford/Princeton and universities in the top 8 to top 12 range. However, only you have the information to calculate whether the expression (expected benefit of getting into a better program*probability of getting into a better program + advantages of the MA at Columbia (network, knowledge, prestige,...)) outweighs the costs of reapplying (MA tuition/costs of living, probably entering the job market one year later, risk of not getting into a program at all,...).
I am in a similar position: I have a fully funded offer from a top 10 university, but I am not entirely happy about this cycle and I am currently trying to get more information on what my chances would be if I were to reapply next year (with a LoR from a methods Prof., more field experience, better GRE)