I've been using Amethyst as my WM for a couple months now, and have used XMonad for significant stretches in the past.
Amethyst tries to bring the XMonad experience to OSX. I think it does an admirable job, but there are some distinctions. Amethyst is simpler to set up, and is more forgiving to newcomers. It has a GUI for configuration, and an easily accessible list of commands. It also works on top of OSX's WM, so it's not so enormous a departure, especially compared to XMonad's fairly extreme dismissal of the mouse.
On the down side, XMonad really outshines Amethyst when it comes to performance. Amethyst is downright sluggish, where I've always found XMonad to be very responsive. Still, it's overall a true enough translation, and the sluggishness rarely actually hinders productivity. Overally, I think Amethyst is a capable daily driver, and a great intro to tiled window managers.
When I had a linux machine I used i3 and loved it. After moving to OSX I search around for a solution and finally found Amethyst. Gave it a solid try for ~6 months or so but recently have moved to using BetterTouchTool with some custom key shortcuts for moving and resizing windows. I've found this works the best for my workflow. I would love to use a tiling window manager for OSX but in the end found Amethyst to be a little sluggish and, as mentioned elsewhere in this thread, buggy for full screen apps. I think ianyh has done an amazing job at working around a system that wasn't meant to be extended in this way, but that puts it at a dis-advantage right off the bat unfortunately.
It is also very buggy around fullscreen apps, enough so that I stopped using it after a week. Slate et al worked much better for me (still slower than TWMs on linux) but forced or at least tempted more setup which is definitely the benefit of Amethyst.
It is super buggy for fullscreen apps. Unfortunately, I have this superpower (or curse) of not being able to reproduce bugs. Every time I get near a coworker's computer, whatever they were talking to me about starts working.
There's a long thread on github about this (https://github.com/ianyh/Amethyst/issues/254). I'd love to know more about your set up. I've been trying for weeks to make it work for people, but Apple's APIs for this are kind of crap. And by crap I mean non-existent. I've started using private APIs to do things like figuring out whether or not the current desktop is a fullscreen app.
I came across that issue and might contribute info in the way of reproducing bugs, but my setup is pretty simple: near fresh Yosemite install, one Chrome window, one Finder window, and two Emacs.app frames (one fullscreen).
Amethyst tries to bring the XMonad experience to OSX. I think it does an admirable job, but there are some distinctions. Amethyst is simpler to set up, and is more forgiving to newcomers. It has a GUI for configuration, and an easily accessible list of commands. It also works on top of OSX's WM, so it's not so enormous a departure, especially compared to XMonad's fairly extreme dismissal of the mouse.
On the down side, XMonad really outshines Amethyst when it comes to performance. Amethyst is downright sluggish, where I've always found XMonad to be very responsive. Still, it's overall a true enough translation, and the sluggishness rarely actually hinders productivity. Overally, I think Amethyst is a capable daily driver, and a great intro to tiled window managers.