Firefox 23 is already available in the stable channel. It doesn't bring that many new features, but it does come with some changes. A small change that may irk some users is the new "unified" search experience.
Changing the search engine in the search box or the address bar now modifies it across the browser, i.e. in the search box, in the Awesomebar and in the right-click context menu for selections.
This is a good idea for most people who would expect to use the search engine they set everywhere that search is available.
But it's not a great change if you prefer to have different search engines in different places, for example, if you only temporarily switch to a new one in the search box and don't want to make the switch permanent.
Search engine keywords
Luckily, you still have some choices. The simplest is to use keywords for search engines, this way, you can still use any search engine you want in the address bar regardless of what you've picked in the search box.
But this involves a few additional steps, you have to pick keywords for the search engines you use, and then you have to type those keywords every time you want to use that engine.
For example, if you regularly use Google, but want to do a search on Bing, you first have to define a keyword for Bing. Click on the search engine drop down menu in the search box and click on Manage Search Engines.
Then, select Bing, click on Edit Keyword and pick something simple, such as "b." You'll then be able to type "b" in the address bar, add a space and then your query, to have it run on Bing and not Google, which will remain selected in the search box.
Revert to the old style
If this is too much effort for you, you can install the keyword.URL Hack! add-on that will revert the change in Firefox 23 and enable you to keep different search engines in the address bar and search box.
You may need to first add a search URL for the address bar in about:config. Type about:config in the address bar, then right click in an empty space to create a new String key.
Name it keyword.URL and set its value to "http://www.google.com/search?ie=UTF-8&sourceid=navclient&gfns=1&q=" or any other search URL you want, like "https://duckduckgo.com/?q=".