This must be second only to "Do I have a chance of getting into Oxford with these terrible grades?" as the most FAQ in this forum.
I don't know where you have obtained the figures you quote - the stats quoted on the University website for 2015 indicate that, for all subjects, Balliol has an acceptance rate of 12% (accepted at Balliol), and an overall acceptance rate of 18% (accepted at Oxford), whilst Lincoln's figures are 17% and 19% respectively i.e. for all subjects, there is only a single percentage point difference - easily small enough to be the result of random variations.
In any case, the answer to your question is that choice of college makes no difference to your chances of getting an offer. If you are good enough, you will get into Oxford.
So - apply for the college you like best, and try not to fret.