I have a feeling it would have been more gritty if Moore had his way.
Probably, but Moore would never have gotten his way, UPN would never have allowed it.
Braga wanted the show to be grittier and have story arcs too, in fact his original concept for
Year of Hell was to have it last all of season 4 with no reset-button at the end. UPN shot it down because they wanted the show to be lighter and episodic. By the time that Moore joined the staff in season 6 the likes of Braga had already been broken by UPN, and they were willing to produce the show that UPN wanted rather than stand up for the type of show they wanted to do.
Michael Piller left as head writer at the end of the second season for a similar reason, he was tired of the old Trek formula and wanted to make Voyager grittier and serialised, so he pushed for the Kazon arc. UPN didn't like it, some other people in the writing staff didn't like it, and many of the fans didn't like it (because the Kazon were pretty stupid as villains) so Piller left and Jeri Taylor took over. She supposedly didn't want Voyager to be serialised, so she rewrote
Basics Part 2 to kill off that storyline and turned season 3 into "TNG in the Delta Quadrant". By the time that Braga took over the show in season 5 it was too late to change Voyager, it was what it was.
Moore thought that he'd be able to change it, he thought that Braga would back his attempts to make Voyager into a more serious show, but Braga rolled over and made the show that UPN wanted. So Moore walked. In my opinion, he was dumb for going to Voyager in the first place, he should have just left the franchise like all the other staff-writers from DS9 did.