My two (hundred) cents:
I mostly play for the narrative (storyline, characters, dialogue, setting, overall look and feel, immersion, etc.) first, the gameplay (mechanics, loot systems, skills, gear variety, drop rates, game balance, etc.) second. As such, I feel very strongly that the narrative in BL2 is superior to BL3. I also feel that the BL3 narrative is sub-par or broken, creating an even wider gap with BL2.
I will not go into details on my narrative opinions here as it would constitute an entire new thread. I will, however, mention that I think they missed the mark on Claptrap’s personality. They should have gone with the one they used in the YouTube videos. Have him really go overboard. That would have been funny and kept him more relevant, I think.
But narrative is meaningless without the heroic character at the center of the story. In other words, the vault hunters. For me it is all about the look and feel of the VH character that I am playing (I am an old school, paper and pen RPG kinda guy) as they relate to the narrative environment.
BL2 had the overall theme of “Badass”. That was something I could easily get behind as a player (“Yeah, I’m a badass!”). NPC dialogue supported the concept of Badass as something to aspire to and be proud of. There were even Badass Points as part of the endgame progression to support this. I always feel good about playing a BL2 character.
The primary theme in BL3 is “Mayhem”. I am having a hard time connecting as a character with the concept of Mayhem. Mayhem seems to be what the Twins engender in their followers and the chaos they sow throughout the galaxy. Not something that I really want to aspire to. But GBX keeps promoting the hell out of the concept of Mayhem as being central to the enjoyment of the game. So… how am I supposed to react to that as a character? Connecting to Mayhem undermines my validity as a heroic figure. But that is what GBX wants me to connect to. 
But BL3 has Guardian Ranks, right? OK, cool. So maybe we are supposed to feel like “Guardians”? Yeah, Guardians of the Galaxy! Woop, woop! We are here to crush those pesky Twins and their chaos-inducing Mayhem. Go Guardians! OK, so where is the supportive, validating dialogue about how being a Guardian is a good thing. Oh yeah, there is a little bit after the main game during the trials when the actual Guardian talks about how sucky it is to be a Guardian and about how you as a VH are now basically being groomed to be a slave of some sort to the Eridians. Yippee… 
So the game’s main theme support’s the bad guys and not the good guys , and the only characteristic left (Guardian) is one that the game itself warns you to steer clear of. Doesn’t make me want to rush out and roll up a character. (You could write a whole White Paper on how this situation is reflected in the treatment of Ava versus Lilith in the storyline, along with the replacement of Badass as the favorable theme - i.e. Maya’s death. If you really wanted to get in-depth, you could talk about how current Millennial cultural values are replacing the late Boomer cultural values and tie that to how the Twins and Ava represent the game’s subtext of millennial heroism. But I digress…).
Speaking of rolling up a character, BL2 had 6 different VHs to choose from (as did TPS), giving me 6 different narrative experiences. Remember, for me Narrative = Fun. BL3 has only 4 and that feels like taking a step backwards. The skill trees of BL2 made each VH feel unique and helped me to shape their personality. The extra skill trees of BL3 make each VH feel more like a character class than a unique character. I am not playing “Moze”, I am playing “a” Moze (or “a” Zane, etc.). So BL3 has less characters and less uniqueness about the characters for role play purposes. Again, not winning any awards with me with the narrative experience.
On the positive side, I feel BL3 has better overall core game mechanics. I played BL2 just recently and kept trying to slide, not as a combat strategy, just for fun. Slam is not as effective or fun as it was in TPS, but I am fine with it being present in BL3. Mantle is a great new mechanic that I wish they could retro-fit onto the previous games. The guns seem to handle easier. I am fine with the menu system.
I am mixed with regards to the new ability to fast travel without requiring a station to start from. On the one hand, it makes travel much easier. On the other hand, it takes away from the immersion and allows me to simply bypass areas that I would have had to fight my way through if I needed to reach a Fast Travel station.
The annointment system leaves something to be desired. In short, I think they went overboard and should tone it all way down, maybe as far as Luneshine from TPS. If possible, I think they should remove annointments from gear altogether and put them onto trinkets or some other swappable mechanic. I like the overall idea of annointments, I just don’t like the current implementation.
Mayhem Mode - well, I have tons of views on that in other threads. Suffice to say that I like the idea of Mayhem Modifiers, but again I think they dropped the ball on implementation. In short, I think they should separate Mayhem Modifiers from scaling progression completely.
As for drop rates, I feel that BL3 has gone too much the other way from BL2. There are far too many Legendary drops to the point where legendaries no longer feel legendary. I also think that there is a gross imbalance with legendary weapons at the higher end scaling progressions in that most are useless (but much of that could be corrected I think by reducing/removing annointments).
I would like to see Pearlescent gear make a comeback, but I have no high hopes (I would like to see more zero g and jump pads, too). And I would like to see more use of Eridium (like they did in BL2 with paying for Raid Bosses, upgrades, etc. The one vending machine by Earl I find to be pointless).
That’s all off the top of my head (and that took me over an hour or so to put together, BTW).
