HaxeFlixel is a complete game engine, but it is limited to 2D.
MonoGame is a "Framework"; abstracting away a bunch of fiddly tech stuff, but you'd still need to do a bunch of heavy lifting. It does support 3D, though.
Think about things like collisions, particles, animation, camera systems, states/scenes, and tile maps.
HaxeFlixel provides all those, but in MonoGame you'd have to make your own implementations (or find someone else's).