If you search for files by name, size, dates, kind and other directory properties, use FAF, because only then you can be sure that everything available is found, even if Spotlight hasn't indexed it.

FAF can also find textual content if it's uncompressed, as in plain text files and even most binary files. And with the option to include Spotlight results, it can also find text in PDF, Word and Excel documents as long as they were indexed by Spotlight.

Find Any File has a few gems that other search tools do not offer:

Better results: It offers an alternative hierarchical view for the found items. You can switch to it with cmd+2 or click on the "View" icon at the top left of the results window: Note that the search above revealed hundreds of hits. If you'd look at that many results in a flat list, it would be hard to browse. With this new hierarchical view, however, you can directly look for the results in the folders that interest you.

Image Preview: If you're looking for pictures, the image preview browser is helpful as well.

Find everything on your disk: If you hold the Option key (alt ⌥) down in the Find window, the Find button turns into Find All. If you click on it then, you are asked for an administrator password - and then Find Any File will restart in root mode, being able to find really any file on your Mac's volumes, including files in other users' home directories (something that Spotlight won't do). Note that this will only work on local disks, not on network mounts, though.

You can save your entered searches to files (they'll have the extension ".faf"). You can then double click them in the Finder to have them start the search immediately, or use the saved search as a preset.

The found results can be copied to the clipboard or saved to a text file that contains the paths (extension ".paths"), for further processing. You can also open such .paths files again in FAF.

Integrate with Alfred, Keyboard Maestro and PopClip. See here for details.

Hide and unhide individual files and folders (ctrl-click on the found items for a menu).

Delete user-installed locked files that the Finder won't let you trash. (Note that some can't be deleted at first attempt and may require you to reboot the Mac first before trying again, while other files, especially those owned or managed by macOS, can never be deleted due to Apple's security model).

FIND ANY FILE is created by .