Battle mode is sadly a major disappoint compared to past Mario Kart battle modes since it takes place on the race courses, rather than dedicated courses made for battle. It really slows down the game play and makes it so time-out is the most common end to battle mode. I'm glad they allow you to be ghost who can't get points, but can still knock people out of the game.
As for actual online racing: It's great. Save for the moments of Nintendo Lag*. I mostly play with two friends from another forum (I made it my goal to get 100 wins against them both and have gotten it since setting that goal.) I really enjoy Mario Kart 8, save for how the items work. Sometimes despite being further behind, you still get worthless items for your situation.
*An example of Nintendo Lag: I was racing on Donut Plains 3 today. On the final lap, I was in first and had finished the race. However, I did not get first on the results screen. I ended up with second place, while the person in THIRD, note not the person in second, the person in third, somehow got first place.