Your web browser history is something you should be able to take around with you, no matter the browser you use. Unfortunately it is not in any browser’s best interest to talk to each other, so you must rely on a third party to get the job done. Infoaxe does the trick.
This add-on for Firefox will save full text web history (and make it searchable). They pretty much log all the websites you browse though, and then create a search engine where you can search through pages you have visited before in the past.
This video does a great job at explaining the basics about Infoaxe:
Overall, it is a neat tool and takes a different approach to this age old problem of getting your browser history in sync. You can download it and try it out via the Firefox Add-ons web site.