I consider myself a huge Halo fan so I apologize in advance for the short essay that is about to follow.
I think the constant comparison is really tough. There are plenty of hardcore Halo fans like myself that really did not like some of Bungie’s design decisions; the Halo 3 BR spread, Bloom and Abilities in Reach, ignoring the competitive community, smaller scope of Halo 3’s story after 2, etc. Unfortunately there is such a stark contrast between Bungie’s titles and 343’s that the issues with Bungie’s titles get ignored simply because they are nuances compared to the sweeping changes that 343 made. When Halo 4 came out it was so different even from Reach that we now have a debate over “classic vs modern” Halo as opposed to debate over how to strike the best balance with minor sandbox tweaks. If you visit other games’ subreddits there is usually debate over whether weapon X is too powerful or if Y is a bad map. If you look at Halo’s subreddits or communities online the debate is over whether X title ruined the story or why key gameplay mechanics are even in the game, often comparing 343 and Bungie directly. Personally I believe there are 4 key areas in which 343 and Bungie differ.
Gameplay: When Halo Reach introduced armor abilities including sprint there was an incredible amount of pushback from the fans. At the time the majority of Bungie had moved onto what would become Destiny and a newer team was left to take over Halo. In retrospect Reach actually feels like a testbed for a number of mechanics that would later make their way into Destiny. Halo 4 and 5 both took these mechanics, including sprint, and dialed them up to 11. The movement in both 4 and 5 is incredibly far removed from Bungie’s titles. Unfortunately Halo’s core does not work with these movement changes-the long time to kill, map sizes, weapon balance etc does not work with sprint. There is a reason why games like COD, Battlefield, Siege work with variations of sprint whereas games like CSGO, Overwatch, Valorant do not. This mix of mechanics in Halo doesn’t work 343 needs to either return to the classic formula and innovate through the sandbox or fully change the gameplay to mirror COD. I think most fans would prefer the former. There are many youtube videos cover why ADS, Sprint, Charge, etc don’t work in Halo, the ChrisRayGun one above highlights many of these arguments.
Art: There was a big change with the art in between Reach and 4. 343’s games feature a fundamentally different style. After over a decade of games and other media the shift in art was jarring and made it feel like the games lacked continuity. It simply did not feel like Halo too many fans. 343 has seemingly reversed course with Infinite and while there has been a general return to Bungie’s style a lot of the plastic and blocky appearance of 343’s carried into Halo Infinite. It’s still just not quite there.
Music: It is incredibly hard to fill Marty’s shoes. He is an incredible composer and Halo’s music has always been in a league of it’s own. Halo 4’s soundtrack was decidedly more electronic and far removed from the Bungie’s titles. This furthered the feeling of a lack of continuity between games. Halo 5’s soundtrack moved closer to Bungie’s titles but still lacked the weight and emotional impact of Marty’s music. Halo without Marty’s soundtrack is like watching Star Wars without William’s score. It just doesn’t feel right.
Story: This is the other big one. 343’s games expanded the mythos greatly. Unfortunately I do not feel that it did so in a satisfying way. Bungie had this Human-Forerunner relationship that was shrouded in mystery. It heavily suggested that the forerunners chose humans as their “offspring” or that humans themselves were forerunner. 343 took this idea and spun it on its head with a “plot twist”-the humans and forerunners were actually ancient foes with the forerunners being split over whether they should choose humans to replace them as the galaxy’s caretakers. Some really enjoy this “twist” but I disagree with the direction that they chose. Bungie had been careful with the forerunners and relied heavily on allegory. 343’s lore broke a lot of the foreshadowing that had come before. Moreover much of this lore is required to understand Halo 4 and 5. I was a huge fan of the Halo novels but always appreciated how they expanded on the world in the games. The games were something that my casual friends could jump into and understand the story without any additional lore needed. Finally, 343’s stories have been built around personal conflicts and relationships. This included some odd changes in character between Bungie’s games and 343s, the new romantic Chief-Cortana subplot being the worst of these. Halo 4 is the story of Chief and Cortana’s relationship, the Didact vs. Chief, and Chief vs. UNSC. Halo 5 is the story of Chief vs Locke and Chief vs. Cortana. This contrasts greatly with the focus of Bungie’s Halo games. With Halo 1-3 focusing on humanity’s war with covenant, uncovering the mystery of the forerunner, fighting for survival against the flood, the covenant civil war. In Halo 1-3 Chief, Arbiter, and the main characters are all actors in this larger conflict whereas in Halo 4 and 5 the main characters are the conflict themselves.
There are so many things I have skipped over but this post is already too long. I could fill a book with my thoughts on how drastically different these two versions of Halo are. The crux of all this is that 343’s games have been a stark contrast with Bungie’s games. There is a distinct lack of continuity in nearly every regard-gameplay, art, music, story, etc. The 343 games are not bad they just do not adequately fill the role of a sequel; they feel like a stark divergence from the previous titles. It is kind of like seeing the lineup in your favorite band change after a big argument. Their new album won’t feel like the same band. They may even show up and play the old hits at a concert but it doesn’t feel the same.
Halo fans like myself are often accused of "hating new things". I always take issue with that. More than anything else we just want continuity; we want a sequel. There are plenty of ways to evolve and iterate on Halo without feeling like a different series entirely.