To prevent any arguments over this somewhat "sensitive" matter, I'll keep my post free from my own opinions and only state the facts.
Avant is a front-end for IE. Firebird automatically imports IE's favorites folder into it's bookmarks, so I assume it should do that for Avant as well, unless Avant stores your Favorites in a different place. Even then, you should be able to use the Import option in Firebird's bookmark manager to load Avant's favorites file. I'm not sure about this, so you should probably wait for a confirmation from someone who has done this already.
As far as security is concerned, again, Avant is based on IE, and is thus affected by all the ActiveX and other exploits that IE is affected by. Firebird is based on the Gecko rendering engine, and does not support ActiveX out-of-the-box, making it more secure.
What can Firebird offer that Avant can't? Well, I haven't ever used Avant, but I just had a look at the feature list, and it includes some of Firebird's basic features such as tabbed browsing, popup blocking etc. However, one HUGE advantage Firebird has is it's extensibility due to it's open-source nature. There are so many extensions available to make the browser more functional, it's unbelievable. If you want to do something, chances are there will be an extension available for Firebird. If not, you could request it on the MozillaZine forums, and if it becomes popular enough, a developer will probably code it in no time. That's the power of open-source applications.
Firebird also uses the Gecko-rendering engine, unlike Avant, which uses IE. This means that Firebird renders standards-compliant code the way it's meant to be displayed, while IE will frequently distort certain parts of correctly coded sites; it especially has some severe rendering bugs when it comes to CSS (and of course, the infamous PNG transparency). That's not to say Firebird renders every site perfectly. In fact, it doesn't, but chances are if it's not rendering correctly in Firebird, it's been coded incorrectly using non-standard or proprietary HTML/CSS code.
There are many other points I could bring up, but it's past midnight, and I'm tired now. But the bottomline is, every person has a certain preference. I have started telling people that
the best browser is the one you are most comfortable with, since you will be most productive when using that browser.
I suggest downloading Firebird and giving it a shot for a while. It may seem different at first, but don't be daunted by it. Stick with it for a few weeks, ask questions in the Firebird discussion thread if you have any queries or problems and we'll be happy to help. Some people love Firebird, while others hate it. After giving it a try, you'll be the best judge to decide whether you want to continue using it or whether you want to switch back to Avant.
That's all I have to say.