i don't think people understand your question
I think other people might be confused as to what you're looking to do.
You were comparing AOL who sells internet access and has their own connection software & own browser with firefox, the name of a browser.
But I think what you were really asking is
should you change the company you receive internet access from.
Some good options include Your local phone company, your local cable company,
yahoo earthlink etc.
I'd recommend you choose one of the local options as they would probably send a technician by your house to set it up.
Once who is giving you access is out of the way you have several free options for what browsering software to use. Firefox, Opera and IE7 are all good options.
Also you would probably want to get an email program, like thunderbird or the one opera has in their browser. It's not 100% necessary to have an email program on your machine, alot of the time you can acess your email through an online account like yahoo, hotmail or google.
BUT before you leave AOL
you should upgrade to their newest browser. It looks like to be very conviently organized into a 4 pane view, with address, chat and browser all in teh same view.
http://www.washingtonpost.com/wp-dyn/content/article/2006/10/14/AR2006101400091.html