FXAA is a image effect, it is not aware of the 3D scene, put rather just the pixels in the texture. Because it works with the pixels of the image, it has to rely on some shader tricks to detect what is an edge and what is not. This is unlike MSAA, which instead samples the scene multiple times to provide anti-aliasing.
Depending on the implementation used to detect edges, FXAA can look pretty good, but depending on the textures used, the geometry used, and other factors (like transparency), FXAA can get confused and apply anti-aliasing to the wrong things or not apply it to the right things.
FXAA can have better performance in comparison to MSAA, as the performance of FXAA is largely dependent on the size of the screen, not the complexity of the scene like MSAA. However, performance varies depending on the complexity of the FXAA edge detection shader code.
If you are curious about FXAA, I would highly suggest searching things like "FXAA vs MSAA" and "FXAA how it works" in a search engine (like Google) and explore the results.
Doing research and investigating what is available will help give you an idea on what is best for your project.
You can find a FXAA effect in Godot, written by the team developing Hight Hat with Godot: Link to GitHub Gist.
SMAA is pretty simple and gives the best results, but is extremely heavy on performance. The idea behind SMAA, as far as I understand it, is to render the game at a higher resolution that the display, and then resize it down to the size of the display. This will interpolate the colors and reduce jagged edges.
The huge issue with SMAA is that you have to render the game at a much higher resolution than what will be outputted to the player for it to look nice. This means the GPU will have to work extra hard to render the scene at a higher resolution. For example, to use SMAA on an 1920x1080 (HD) display, you would have to render the screen at 3840x2160 resolution to have SMAA x2.
SMAA is a brute force approach to fix jagged edges, and because of that is one of the most inefficient solutions (though visually it is probably the nicest looking). As far as I can tell, there is no SMAA for Godot, with good reason because for many real time applications SMAA is simply too performance hungry.
Again, if you are interested to learn more, you can always search something like "SMAA vs MSAA" and "SMAA how it works" in a search engine and explore the results.