The data
The majority of studies have found no effect of forearm position (supinated vs. neutral vs. pronated with or without rotating handles) on biceps activity during pulldown variations [1, 2] or pull-up variations [1, 2, 3]. The only study that directly supports the use of a supinated grip over a pronated grip is Youdas et al. (2010): chin-ups with bodyweight caused higher biceps activity than pull-ups. Chin-ups with a rotating grip were on par with regular, fixed-bar chin-ups.
The dataThe majority of studies have found no effect of forearm position (supinated vs. neutral vs. pronated with or without rotating handles) on biceps activity during pulldown variations [1, 2] or pull-up variations [1, 2, 3]. The only study that directly supports the use of a supinated grip over a pronated grip is Youdas et al. (2010): chin-ups with bodyweight caused higher biceps activity than pull-ups.