Godot is very different. It's closer to a Unity competitor. Most games, should go with Godot. LibGDX is more low level. It's like a java wrapper around OpenGL

Godot is very different. It's closer to a Unity competitor. Most games, should go with Godot. LibGDX is more low level. It's like a java wrapper around OpenGL with some nice libraries for: math/sprites/algorithms/gc-friendly data structures/other structures (octrees etc) and abstracts away platform specific details in most cases so you can have the same code for android/ios/desktop/web. Ingress is also LibGDX, but they switched to Unity for Pokemon GO.