This is a hard question to tackle all at once.
But I guess I can get started.
The biggest and largest plus is the combined Mortal Empires Campaign. It essentially mixes the maps of both games to create one large MEGA CAMPAIGN.
All the races you bought in the first game are also playable in this campaign (except norsca. Due to a lot of reasons that are hard to summarize, they wont be playable or even implemented until May 2018)
Apart from this, the game has a lot of improvements.
The UI is far better, specially the notification system, but its a lot of little things. Just to name a few of the UI improvements I liked: Better representation of your standing with other factions on the diplomacy screen, you can actually see when enemy units are broken or shattered without having to mouse over them, you can set which factions you want to see display of their moves when you end your turn (Unlike the first game, where you either see them all, or disable them all. Here you can pick and choose which ones you want to see or not)
You can now change the direction of spells
You can capture and occupy any settlement in the map like in previous Total War games (In the first one, you could only capture certain settlements as certain races, for example, Dwarves can only capture dwarf cities and orc cities. This was replaced by a climate system, where certain climates are more suitable to your race, and settlements in those climates confer certain bonuses, while settlements in unsuitable climate confer several penalties, but all settlements are capturable)
You can also engage in treasure hunts when exploring ruined settlements. They're nice little RP scenarios that can give you rewards or punishments depending on what choices you pick. You can also engage in treasure hunts at sea, where random mini-isles and sea creatures spawn, and upon going to them, you get a choice of rewards.
Speaking of the sea, there's a weather system in place at sea, where at random, segments of the seas become more tumultuous and raging (With tsunamis, and wicked storms) or calmed and soothing (with extra wind speed), which makes planning your sea routes a necessity, specially when you get caught up in a random storm.
There's also Rogue Armies. These are kind of like mercenaries. They're horde mini-factions with some pretty wacky compositions (One example of a rogue army is a group of fallen bretonnian knights, along with vampiric blood knights. Another is a 20stack army made entirely of rocket batteries, gyrocopters, and steam tanks). They're mini-factions that can be friends or foes, their goal is to try and take a settlement, set down roots and become actual factions in their own right. They can spawn at random at any point, and there's over 50 different combinations of them (my favorite one, is a group of lightning worshipers made of Lizardmen Kroxigors, and Dragon Ogres from the Warriors of Chaos. This group can seriously kick ass)
The main campaign of Warhammer 2 (Called Vortex Campaign) is the first time I can think of, that a Total War game has an actual plot. With cutscenes, characters, plot twists, and such.
WAY better combat animations. Seriously, they look cool as fuck. Including custom animations for the more badass creatures for when they fight other monsters. Such as a dragon suplexing a T-rex, or a hydra tearing the shit out of a poor soldier. The animations look even more sick with the blood and gore DLC.
There's more map variety. As much as I loved WH1, the maps were very samey. There's a hell of a lot more variety in terrain and topography this time around. Including choke-point/bridge defense maps, which were sorely missed on the last few Total Wars.
4v4 free for all multiplayer is back.
A new mode called "The Laboratory" is incoming. Watch the trailer on youtube, its fucking stupid, and awesome, and I can't wait to play it.
The second game is just better.
It took all the best parts of the first game, improved on a lot of its flaws, and added quite a lot of polish. Plus the new races are insanely cool. All of them. And I wholly recommend you to get it ASAP.