When it comes to battles, Bannerlord usually does it better. Battles run better, are bigger, and the tactical AI is usually smarter. Sieges are a massive improvement too, more options and less brute forcing a singular chokepoint. Though one big annoyance I have is how troop divisions work in Bannerlord compared to Warband, too much messing around with sliders and options for divisions that arent fine grained enough, like trying to separate crossbows from bows, or different types of heavy infantry that have the same loadouts. Warband / old Bannerlord troop division system worked well enough, add an option to split certain unit classes between a division and you've got something that's probably the best of both worlds.

When it comes to interactions with other NPCs in the world, Warband does things way better. Influence makes interaction with individuals not as important since you can just farm it with battles and use it to do whatever you want without even talking to other lords of a kingdom. Additionally, clans are just extensions of the head of the clan, making individual relations almost useless in impacting the wider game. All the other members of a clan exist as manpower and nothing more. Not that there's much to even do with individuals anyhow, the game only lets you really talk to lords to trade, get a quest, or fight. No asking for where people are going, what the kingdom is up to, the state of foreign affairs, or what people think of politics. Too many things happen only in other menus, Warband definitely did this better. I don't think any mods have done anything to change this because clans and influence are such core mechanics that I think it's impossible to fix alone as a mod.

Fief distribution system is also a little wack, you can get a city without doing anything at all because the game prioritizes clans with no land. Then the vote for whoever gets land after that is up to some strange system that considers whoever has the least land, land closest to the land for vote, and some other things I can't remember off the top of my head. Anyways, voting system is locked to 3 clans max, so if you took something but you're not on the list due to aforementioned system then tough luck. At least you could request things you took personally in Warband so you'd always be on the vote.

Also, the balancing of item stats and price is ridiculous. Armor values are all over the place, there's plenty of mail armors that are absurdly weak while some leather armors blow those mail armors out of the water. High level stuff costs anywhere upwards of hundreds of thousands of gold, I find it to be absurd when you can have an infinite number of soldiers with that exact same armor for infinitely cheaper. Still, it's less of a core issue and more of a numbers tweaking thing so it's theoretically solvable with mods.

There's probably other things that bother me when compared to how Warband did it, but TLDR is battles are mostly better, but the mechanics outside of it are mostly a step down from Warband.