I've played 25+ battles at this point. The majority were skirmishes. They were typically unit-specific, with no more than 3 units. These were mostly a way to test out common scenarios that players are likely to see on the board.
However, I'd say at least 20% of my games have been what we used to call 2.5k or 3k battles. The game scales up extremely well, and a lot of units really begin to shine when they're fielded in numbers that would only be practical in large games. Factor in unit formations for charging, screens, tactical retreats, characters, etc. and I think that you'll find that a game becomes more dynamic as you add models. The game has been accused by many for lacking tactics and/or being simple, but I have found this sentiment to be entirely baseless.
Now, I would familiarize myself with AoS by starting off playing skirmishes. Your first few games will likely be bloodbaths in the middle of the board until you develop a sense of the game's flow, and discover the tactics that work for you.
For me, it really has been great so far. Coming up with formations, maneuvers and tactics has been a very rewarding experience, and it's exciting to have more diverse defensive options, but also a wealth of explosive offensive ones in a game which greatly emphasizes the importance of the movement phase.