LÖVE is free, open source, runs on desktop and mobile, local builds and so on. Also, it is based on SDL2 so, if you know C, you can modify the code.

That being said, Corona SDK is probably more mature for mobile. Personally I prefer LÖVE because of the fast iteration cycle do to local builds (Corona SDK builds the game on their servers).

Love is a bit more 'low level' than Corona. In LÖVE you have direct control over what gets drawn each frame, wheras in Corona you are more working with a scene graph (nested display objects).

I've used both for hobby games. Corona is user-friendly and it's a great solution with lots of community plug-ins and support. It uses a freemium model, offering features like access to native API's and offline builds at a price, and you can't really use it on Linux. LÖVE is free and open-source and adding support for Android and iOS makes it even more attractive.

Love is used mostly to prototype games for the PC, and support has only begun today of the mobile frontend. (It was usable for a while, but only now is it supported.)

Love has minimal bindings, basically only enough to make use of most of SDL and OpenGL. It lacks all of the native and GUI support of Corona (except where you write your own C bindings... have fun with that, I suppose.)