I don't know about overall, but when it comes to just Halo, between Bungie and 343i I choose the latter. While Bungie made better campaigns, 343i was better when it came to weapon balance. Halo CE's weapons were fine in Campaign, but MP was dominated by that game's OP 3sk pistol, and in subsequent Halo games during the Bungie era the MP was likewise focused too heavily on mid-range "utility weapons" (i.e., the BR & DMR). 343i retooled the AR and pistol to where they're effective starting weapons but that still encourage map traversal and trying out weapons picked up off the map instead of constant cross-mapping with one's starting weapon. Halo 4 might have allowed for BR & DMR starts, those weapons weren't the end all, be all, and the AR could wreck them at closer ranges unlike in previous games where the AR was much weaker. While I have issues with Halo 5, it's mainly about the movement, not the weapons, which all felt great. And after playing the first test flight, Halo Infinite is shaping up to have perhaps the best gunplay in the series.
Outside of Halo, I have generally liked how id's games have played. Doom 2016 was amazing, and I still need to play Eternal.