When comparing SizeUp vs Amethyst, the Slant community recommends Amethyst for most people. In the question“What is the best window manager for Mac?” Amethyst is ranked 5th while SizeUp is ranked 12th. The most important reason people chose Amethyst is:
Amethyst is published under the MIT license making it open-source and id offered completely free. This allows anyone to give the tiling window manger a try, which is great.
Specs
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Pros

Pro Keyboard centric
SizeUp has user-configurable keyboard shortcuts for a set of pre-defined actions.
Pro Supports multiple monitors / spaces
Windows can be sent to different monitors and spaces. It can also be aligned as needed.

Pro Simple
SizeUp is easy and simple to use without having to configure.
Pro AppleScript support allows extending functionality
AppleScript permits adding features such as tiling all open windows. Additionally, FastScripts it allows the user to add keyboard shortcuts to AppleScripts.
Pro Menubar dropdown for shortcuts
Learning a bunch of keyboard shortcuts right off the bat may be difficult to remember at first, which is why a menubar shortcut for the app exists with all the shortcuts listed.

Pro It's free and open-source
Amethyst is published under the MIT license making it open-source and id offered completely free. This allows anyone to give the tiling window manger a try, which is great.

Pro Recently updated and rewritten in Swift.
The application was written in Objective-C, but was recently updated and completely rewritten in Apple's new native language Swift.

Pro Works with keyboard shortcuts, no mouse needed
As it's designed to work closely to how xmonad, Amethyst uses keyboard shortcuts to control the windows being used, meaning no mouse input is necessary. This can make for a faster way to control windows.
Pro Multi-monitor suppport
Pro Has many common layouts to choose from (fullscreen, floating, row, column, wide, etc)
Pro Can switch between tiling and floating mode
Pro Under active development
Pro Configured via UI
No CONFIG file provides security and will avoid making amethyst crash. Instead configured via simple UI
Pro True tiling means never losing track of windows under a huge pile of others
Cons
Con Nag window
If a license is not purchased there is a nag window (which suspends function) that pops up when loading the app (at user login). The nag pop-up is also summoned at certain time intervals and by performing a certain number of commands (manually or by keyboard shortcut).
Con No on-the-fly split screen window settings
Unlike some other tiling window managers, SizeUp has no way to change the size of split screen actions on-the-fly. Any time a user wants to change how much room on the screen a window takes up when using the split screen function, they will need to manually change the settings, which can be time consuming.
Con Can be buggy at times
Con There are more user friendly window managers available
There are certainly more user friendly window managers available for MacOS, such as Divvy or Moom. Amethyst, however, is more powerful and customizable than the more user friendly options available and therefore may be a better choice for a user looking for more advanced capabilities and customization.
