Do the smaller gauge guns - 16, 20, 28 - require less or more choke to achieve a given pattern percentage compared to a 12 ga?
They require less constriction.
Choke is a performance - this is definitional. For most choke designations performance is expressed as a percentage of pellets in the 30" circle at 40 yds. Some exceptions: .410s have traditionally been patterned at 25 yards. Modern shotcup loads perform well enough to warrant revisiting this figure. Skeet patterns are usually optimized at 21 yards (skeet out/WS2/SK2 may be optimized another 10 yds out), but in recent years 45%, or so, at 40 yards has been considered "skeet".
Constriction is not choke, though many confuse the terms. Constriction required to deliver a certain pattern percentage varies directly with bore diameter, as you can see from various charts published by Briley, etc. There are other variables: required constriction for a given percentage will vary with payload - as the Purdey website illustrates.
Sam