How to search dconf for keys or values?

First, the search function in dconf-editor searches only among those things which are directly visible on screen or reachable by scrolling (note that the search field looks just like the one in other applications like Nautilus).

I know of no other graphical tool you could use. So you probably need to use the command line tool dconf (also from the package dconf-tools).

Specifically for search recursively through the whole database (including keys and values) I would use this command:

dconf dump / | grep SEARCH-TERM

dump basically gives you the whole database in an "Windows-Ini-File"-like format. For browsing through the database, use dconf list /PATH.

As you've mentioned gsettings, the equivalent search command there is:

gsettings list-recursively | grep SEARCH-TERM

However, this may not be what you want (for a search for unity, this gives completely different results for me). Not sure what database is used here.

Edit: After reading this question, I noticed that dconf shows you only the settings which are actually set in the database, not all possible settings like dconf-editor. Apparently you can use gsettings list-schemas to give you all possible settings.