Good question. Grom is very fun, mainly because of his cauldron ability.

Tomb Kings are top-tier for fun in my opinion.

Not only do they have a great story-based campaign with interesting goals, but the unit caps make it hard to optimise the fun out of your campaign. As long as you can get jar production rolling and rush out lots of armies they won't feel weak despite your inability to min-max army compositions or roll around with doomstacks.

Taurox (heck, all beastmen) are fun for the same reason Tomb Kings are in that unit caps prevent you over-optimising your armies, but also more overpowered especially as your campaign progresses as you will start to roll out doomstacks, and the tools at their disposal are genuinely broken. That said you'll probably finish your campaign goals before this starts to make battles too braindead AFK.

Skaven are universally fun regardless of campaign, and their base mechanics are so broken in human hands that even their weakest lords like Tretch still feel incredibly strong. Ikit Claw, Snikch and Throt are the most fun though because of their unique mechanics and campaign goals. Moreover Skaven can genuinely succeed on any battle difficulty with a pretty broad collection of army types as long as you focus on their campaign map strengths like ambush attacks and rapid tech advancement.

Grom is great because his Cauldron mechanic makes lots of units viable so you can do something other than crapstacking Sneaky Gits and still get great results even on hard battle difficulty.

I also enjoy Repanse because Bretonnians are a strong faction, but fun and micro-intensive on the battle map. No AFK doomstacks or one-note archer spams. Being able to play with cav-based armies and not feel super weak is great.

All the Vampire Coast campaigns are fun, but maybe a little bit too easy once you min-max shipbuilding and can rush out a doomstack. Still fun though.