I've enjoyed my share of quick, fun games on the Wii. When I upgraded to the WiiU, this was the first title I rented. Finally, an enjoyable game for those who've grown up!
Although Arkham Asylum was originally on other consoles, I find having the second screen with the map display, weapon switching and interesting tidbits such as character bios give the WiiU an edge for playing this game. If you find you get lost in wide worlds, worry no more!
If you grew up in the 90's watching Batman the animated series, you will positively be delighted at the familiar voice acting here. The story is engaging, and the visuals have lots of interesting details, if you have a moment to enjoy the scenery.
Onto the action: it's smarter to be stealthy and use your tools (I enjoy those kinds of challenges) but when it's time to clobber, the fighting action has a lot of variety and the difficulty ramps up nicely as you progress. The AI, like people comes in all kinds: goons that you can walk right up to from behind and take out, to surprisingly smart that make you really plan out how to take out the baddies.
Downsides? It might just be me, but with all the controls, occasionally I find myself using the wrong weapon. Using the controls screen for the remote batarang can drive you crazy after a few failed tries. But other than that, there's so much to do, so many side quests you can try, that I'm still happily going through it all.