I think it's incorrect to say just lager or smaller. Too many factors have to be taken into account.

For example for a non-adaptive site the font have to be bigger, and usually browsers do it automatically.

For adaptive sites - the situation is different. If the main site text is about 16-18px, then of cause it should be smaller on mobile, down to 12-14px (which sites usually have back in 14'-15' monitors size era). Since phone screen size is even smaller, so the target font size maybe around see more 11-12px. Also phones usually have retina screens, it perfectly displays small text.

As the conclusion something like this should work in my opinion:
16px - default font size for desktop
16px * 75% = 12px - approximate font size for the mobile

PS: px is very subjective dimension, it translates into very different real size or even real pixels on the screen, so 12px font size on mobile will be slightly different on different mobile devices.