tl:dr, Average =/= Average, thanks for useless statistics game!
I made some more effort in testing this. When making more controlled tests I quickly realized the two bows were indeed shooting at different speeds. But here's some more stats that I gathered at the same time:
Tutorial area, first wolf. Combat in slow mode. Ranger with 3 might and 10/20 dex, bear tanking while spamming stop command. 5 shots, (including recovery time after).
10 Dex
Hunting bow: 5 shots 24,4 sec. @ 5*12,5 dam. (avg) = 2,56 dps (x2 for normal speed)
War bow: 5 shots 36,5 sec. @ 5*16,5 dam. (avg) = 2,26 dps (x2 for normal speed)
20 Dex
Hunting bow: 5 shots 18,5 sec. @ 5*12,5 dam. (avg) = 3,38 dps (x2 for normal speed)
War bow: 5 shots 27,0 sec. @ 5*16,5 dam. (avg) = 3,06 dps (x2 for normal speed)
Clearly the Hunting bow shoots faster. The War bow does slightly less dps, but should still be better because of damage reduction being less effective against few strong attacks versus many weak ones. The dps almost increases the full 30% at Dex 20, the small loss coming from the actual shooting animation since that is not (?) reduced by high Dex.
Edit: War bow better for raw damage against armored targets, Hunting bow better against unarmored targets or for interrupt builds.
It boggles my mind how such an arbitrary "statistic" as average is put in the middle of all those numbers that actually mean something... not to mention average is not the same thing as average. Thanks a lot!