Sidepulls gave way to centrepulls which gave way to sidepulls, although sidepulls we're always around. The heyday of centrepulls was the 60's, as far as I remember. At that time, and well into the 70's, good bikes had centrepulls and cheap bikes had cheap, troublesome sidepulls. Then that situation reversed for a while into the 80's.

I was never a racer, but most of us at the time preferred centrepull Mafacs simply because the damned things stayed centered. Back then, sidepulls always seemed to end up dragging on one side (and you had to frequently fiddle with them to avoid it).

Assuming tire clearance is not an issue, in my opinon, nothing beats the modern dual-pivot sidepull. More stopping power for the least hardware and the least finger pressure. Centrepulls we're stronger, theoretically, but you did have that bare cable bridge to stretch in between you and the brakes, and you did have to have something to hang them on. Sidepulls look cleaner.