I always found it easier to type "ctrl/cmd-l amazon.com" and do my search than use the mouse to switch engines (is there a keyboard shortcut??) But, knowing that it can potentially benefit Mozilla, I will start using it more often now. Thanks.
I recently found out a life-changing tip with Firefox. Right click any search box on any website and hit "Add keyword for this search." You can then assign a prefix which you can use in the address bar to search that site. For example, I have these set up:
Opera has had this feature forever, since around 2001. Long enough ago that it shipped with search keys for Altavista and Lycos along with Google. The feature was a primary reason I started using Opera in the first place.
Originally you had to dive into a config file to add non-default search providers, but it's now in the UI just like Firefox, right click any text field and select "Create Search".