Recs.
Updated
SpecsUpdate
Pros
Pro Active and helpful community
The libGDX community, in the official libGDX forum is extremely helpful and approachable for any kind of question regardless of the its quality or difficulty.
The forums themselves are a very helpful resource for any issue or guide simply by searching past posts in there.
In addition to the forums, there's also the official #libgdx IRC channel on Freenode.
Pro Free, open source & permissive license
libGDX uses the Apache License 2.0.
Not only is libGDX free and open source but also it's license gives you a lot of power over the engine. As long as you provide a copy of the license, give credit, do not hold devs liable and do not use libGDX logo in any engine forks you can do pretty much anything you want.
Pro Focusing on object pool patterns, to control memory without pointers
Unlike Unity or other engine, it allows to optimize a language that uses garbage collector when using patterns of objects you can control the use of memory without needing a language like C / C ++, getting the same speed in a more productive language.
Pro Fantastic UI toolkit (scene2d)
scene2d is a 2D scene graph, scene2d.ui is a UI toolkit on top of that. It enables very complex mobile and desktop UIs.
Cons
Con Could be difficult for inexperienced programmers
LibGDX is a low-level engine meaning it requires much more coding than other higher-level engines. Although this allows for greater customization, it can make things more difficult for beginner programmers.
Con Documentation could be better
Other than a brief installation / getting started overview, libGDX's documentation consists of an official wiki with several incomplete pages, and automated Javadocs. The community recognizes these shortcomings, and new users are encouraged to ask for help.
Con Performance issues related to Java and the JVM
libGDX is written in Java. While there are ways to build it into native binaries, its intended and supported use is with the JVM, which has performance ramifications.