The Randomonium tavern brawl is a bit more to my liking. Partly because there's no deck building involved.
It's a bit one-dimensional but apart from tactical nous the one piece of strategy is to try and take an expensive card in the initial draw and hope that its cost means it comes out in the first or second turn.
The Gift Exchange tavern brawl seems dominated by mages. I've played as a Warrior, Hunter and Mage and the ability to do direct damage means to you can grab not just your enemies crates but also your own. This means you can get two special cards per turn and your opponent nothing.
I'm starting to hate the Knife Juggler. I'm not sure what you've got to do to get hold of it but unless you use a bunch of Enrage minions it's shockingly annoying.
Garr was really tough until I realised that the Priest's Mass Dispel cancels the explosive effect of the initial minions which means you don't need to care about juggling them.
Add in some Silence spells and some heavy hitters to manage the other minions and do damage and it really wasn't that bad.
The Emperor Thaurissan challenge was particularly interesting with the need to keep one of his minions alive therefore denying the use crowd control cards and having to get used to a steady dribble of damage each turn.
In the end I managed to get a Lightspawn buffed to 10 for a mid-game victory but the gameplay challenge here was building a deck to achieve a goal for the first time, rather than trying to cover the bases in ranked play.
For example, in the League of Explorers I don't think I had ever run out of cards before until I started to hoard the genie's wishes in the Warrior challenge. I don't think I'd ever understood there was a draw limit.
The solo class challenges and "scenario" games are pretty interesting and actually help you understand how the mechanics of the game work and fit together.
After playing in the beta for a bit I rapidly lost sight of the metagame and couldn't compete in Arena or ranked games. But now with the introduction of more solo games I'm back and definitely enjoying it more.