When comparing Caja vs Thunar, the Slant community recommends Thunar for most people. In the question“What are the best file managers for UNIX-like systems?” Thunar is ranked 2nd while Caja is ranked 16th. The most important reason people chose Thunar is:
Unlike Nautilus, which requires the whole GNOME desktop, thunar just depends on some XFCE utilities & GTK.
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Pros
Pro Easy to configure
Pro It has a reasonable set of features, out of the box
Not too much cluttered, but enough customizable.
Pro Caja script extension makes it more useful
Caja script extension adds your script in script menu, then passes the file name as a parameter. This allows you to run operation which is not included in Caja.
Pro Allows you to access remote or local locations
You can click the Files entry in the panel to access a specific location (remote or local), connect to a certain server (FTP, SFTP, SAMBA, etc.), access your bookmarks, open a new window, as well as to change its default functionality.
Pro Open or run as administrator in the right-click-menu of the mouse
Pro It just works
Customizable and clean, this is crushing that garbage nautilus, the overrated p.o.s. gnome destroyed.

Pro Minimal dependencies
Unlike Nautilus, which requires the whole GNOME desktop, thunar just depends on some XFCE utilities & GTK.

Pro Supports "quick-directory" typing
While in a Thunar window, typing either a "~" or a "/" will automatically start typing into the "address-bar" and pressing enter goes straight to the typed directory.

Pro Non-recursive find
In a thunar window, any non-directory typing will search in the current directory for the filename that you type (non-recursive, unlike Nautilus)
Pro Select by Pattern
Select multiple files in the current folder using a wildcard pattern.
Pro Custom actions are easy to set up
Use Custom Actions to add right-click options to do things like Open as Root, Open Git GUI, etc. You can filter the file types and filename patterns that the actions will show up for.
To add an "Open as Root" action, go to Edit, Configure custom actions. Assign a name and a description. Set Command as "gksudo xdg-open %f" (you'll need to install gksudo since pkexec won't work). Pick an icon (I prefer "changes-allow"). Under Appearance Conditions, select Directories, Text Files, and Other Files.

Pro Supports forward/back mouse buttons
Supports the M4 and M5 mouse buttons for forward/back, similarly to most browsers.
Pro Supports renaming files in bulk
With also predefined functions as insert (date, numbering,...), search/replace, etc ...
Pro Split View
Browse files in two directories with a dual pane view.
Pro Does the job
But nothing more.
Pro Keypress to search in folder
While in a Thunar window, typing a filename automatically selects the first matching file in the current folder.
Pro Can assign custom shortcuts to scripts in XFCE
Thunar can use the editable accelerator feature of XFCE.
Run xfce4-appearance-settings
in terminal, go to settings tab, check "enable editable accelerator". Now open any command in Thunar menu, hover to a command, i.e. your custom "places" or your custom command, then press any combination to assign a shortcut to it.
be careful though, cause it will also remove the shortcut from other command.
Pro Tabs
Use tabs to open fewer windows. New tabs automatically start in the same location. Tabs can be detached.
Cons
Con Frequently very slow to transfer multiple small files
Folders move fine, but it chokes on files, where other browsers take seconds.
Con Mostly unconfigurable
There are not many ways to configure Caja to fit your needs. Besides what can be seen in the settings button you can't configure it further.
Con Sort Order / Limited Configuration Options
It ignores special characters when sorting files and folders. Underscore, tilde, bracket, ASCII characters, .... everthing not recognized in numeric/alpha sorting. Also, I found no way to remove the triangle to reveal contents of sub-folders rather than opening... but I did quit looking after several seemly unalterable functionality issues.
Con Very slow to list thousands of files
Unusably so.
Con No integrated search option
Con No usable image view mode
Setting view to "icons" doesn't satisfy. The icons are too small to see the image.
Con Simplified action bar
The action bar on Thunar is very simple and doesn't have as many features and buttons as other file managers. It only has a back, forward, up, and home buttons as well as the folder path.
Con Does not integrate well into Gnome
Con Tree sidepane missing features
When the sidepane is in Tree mode, it does not show Places (Favorites). It also doesn't collapse folders (like Windows Explorer), adding to clutter.
Con Requires GNOME dependencies to support common features
Thunar relies on GVFS to support mounting disks or accessing web folders, however since GVFS is a third party GNOME library and made for the use in the GNOME environment its often incompatible to Thunar stable releases which results into crashes and other issues
Con No double pane support
Working all in all quite good out of the box, but the windows are too big. Drag & drop is working, but useless on a one-window file manager. Even for novice users it's too weak for everyday work.
Con Requires plugins for some basic functions of modern file managers
Con No Split View without a patch
Which can be a deal breaker.
Con Moving files
Has serious problems moving files. It may stop abruptly with some undefined error message and the files would be gone afterwards.
Con Won't write to any removable media that has been on an Apple machine
Removing dot-files that Apple puts on the media (like .fseversd) allows Thunar to write to it.
Con Doesn't integrate well with archive manager other than Xarchiver
"Extract here" function doesn't integrate well with archive manager other than Xarchiver (e.g. Ark, GNOME Archive Manager).
Con Image thumbnails sometimes wrong
There seems to be a bug where sometimes images get the wrong thumbnail, this can lead to data-loss.
Con Slightly unstable
Thunar crashes some times on file moves, copy-pasting etc. The developers are working on it, but it's taken a while.
Con No progress bar when copying/moving file
Either this is problem with XFCE4 or Thunar, but there's no progress bar when copying/moving file with Thunar.
The only way to tell whether it finished is CPU usage.
