Morphological Anti Aliasing was initially created for its use in consoles, where you have a very limited performance budget, but with the advent of deferred rendering pipelines (DX10,DX11) they are becoming more popular to use due to the complexity of using FXAA as a separate process for lighting and geometry (deferred render pipeline). Its simply not as good.
The morphological AA is a post-processed technique (post-pipeline), it takes the frames out from the end of pipeline and then runs a search and fixes aliasing found. This has the advantage of a very low impact on performance and it also fixes transparent texture aliasing which multisampling fails to do.
It has a performance impact of around 5%, or 10% in extreme cases. Usually less. It uses compute shaders rather than bandwidth like classic expensive multisampling.