NME implements the Flash API over OpenGL. NME is almost always accelerated. This is why NME performs much faster than standard Flash content that does not take advantage of Stage3D.
Starling is a library for Flash Player that tries to implement the traditional Flash APIs over Stage3D, for 3D acceleration, but it is still notably slower than NME. Again -- this is NME without using a special 3D API.
OpenGLView is a new class, available with NME 3.5, that provides access to OpenGL in a DisplayObject. It is not required to be underneath other DisplayObjects. It provides a great amount of flexibility.
Wighawag has helped implement Stage3D as a compatibility above the OpenGLView class, so that we can support more content which targets the GPU for native NME platforms (which NME does by default) and also targets Stage3D for Flash Player.
Nicolas' H3D and H2D may become a replacement for something like Starling, and may be compatible with NME in the future (I am not sure what the current state of the project is, currently)
OpenGLView might be made available for WebGL, but most browsers have WebGL disabled by default, which lessens the value of it.