In VOY and ENT he wasn't really in charge, "Exec Producer" there just meant he was the designated target for audience rage.
That's not exactly true. In seasons 5 & 6 of VGR and seasons 1-3 of ENT, Braga was the showrunner, meaning the head of the writing staff, the person setting its creative direction. Although in the latter case, Berman took on the role of co-showrunner, participating in the writing process far more directly than he did on any of the previous shows. Prior to ENT, the only actual scripts Berman had done had been "Brothers" and "A Matter of Time" for TNG; otherwise he'd only contributed to the occasional story outline. He mostly handled the logistical side of the production and left the creative side to his showrunners (though he still had final approval). But on ENT, he took on the role of Braga's regular writing partner for the first time. And I consider that to be the most likely reason why ENT was so inferior in the writing department -- because someone who wasn't a very experienced writer was taking a direct hand in the writing. Berman did a great job handling the logistical side of Trek production, but when he crossed over into the writing side, he was out of his area of expertise and it showed.