Is Mozilla better: - YES
Safer : - Haven't a clue, but should not be any worse because it still works behind your firewall and antivirus/spam programs).
I have found IE almost impossible to use over the last year because it 9 times out of 10 hangs!
Mozz has never hung - and for that reason alone wins. I can't see any minus points: it looks the same, and if you like, can be customised till the cows come home.
The best thing is to give it a try - the two programs do not interfere with each other.
I have been using Firefox for a year now and would not even think of using IE now, especially IE7 which I detest. As Mike says, if it's working behind a firewall it should be safe enough and I certainly have not had any problems at all.
There are lots of add-ons available for Firefox so you can customise it to your own liking. Certainly worth downloading and running.
Firefox all the way. I.E. is a Gates product, people hate Gates, ergo people look to exploit I.E. more so imho. Loads of great custom features in FF as mentioned. Heck, it's free, try it and see.
IE has the worst security record. It is vulnerable to attack by allowing a website to run script or install BHO's without you knowing.
Firefox grew out of open source software and is by far less vulnerable. There are add ons like NOSCRIPT to monitor java script ( I use this) and Foxcast for weather etc.
It does not try to take over your browser run you.
Give it a go you wont be sorry
Firefox gets my vote as well, I use it with 'NoScript' which does take a bit of getting used to, coloured Tabs, spellchecker, screensaver, and Ebay companion.