the COLREGS it seems are for establishing blame after the fact. I haven't spent any time on a commercial ship's bridge to see what actually transpires there. But I assume they have ARPA and AIS alarms set, and occasionally glance away from the magazine or DVD they are looking at. I'm talking here about uncongested space, obviously not entering harbors where one would hope a more active watch would be on. In that context they are likely to get (and believe) the AIS alarm first since radar is a fuzzy view of the world.
Starting from scratch I would install the AIS transponder before the radar transponder without question. But these days I wonder if the radar transponder still has any merit? Certainly for small boats, which might have radar and no AIS receiver, but for big ships? Small boats would be covered by X band.