I honestly think when the TNG writers were divided between DS9 and VOYAGER, they put them where I think they could thrive the most.
Rene Echevarria and Ronald D. Moore were excellent at characters and their interactions, which is what DS9 was best at. Considering how many secondary characters were created in DS9, to juggle that many characters needed writers on staff who were best at writing those traits.
Brannon Braga was always a high concept writer. I did notice he dove into the time travel well too often... I did a count of all his credited STAR TREK episodes a long time ago, and about 1/2 - 1/3 dealt with time travel in some way and that may not seem like much, but he was credited in nearly 100 episodes, which means at the very least about an entire television season was time travel related. That sounds a little time travel obsessed to me.
Despite that, Braga was very imaginative and he did some really good scifi concepts, and VOYAGER needed someone like that from the start. The Delta Quadrant needed a way to separate itself from the Gamma, and just look at the odd sentient lifeforms encountered in season 1. A living nebula, a photonic lattice, disembodied entities (Which has been done before in STAR TREK, but the twist with Chakotay was refreshing.), space dwelling lifeforms, and a twisting distortion. Particularly since VOYAGER was launching a new network, it needed someone like that to draw the audience in.
Later, Joe Menosky was brought on, and he and Braga were a good pair. Joe helped ground Brannon, and that helped make some really great episodes... "DISTANT ORIGIN", "SCORPION" two-parter, "YEAR OF HELL" two-parter, "TIMELESS", and others.