Actually, I run Tiger 10.4.11 on my iMac at work, Leopard 10.5.8 on one home MacBook (white circa early 2008) and Snow Leopard 10.6.7 on a second MacBook Pro at home. I'm running the gamut on three different Macs! At work especially, I live by the creed, "if it ain't broke, don't fix it". If you are happy with what you have and your computer and OS meet your needs, why change? No need to if it all works for you.
I very much prefer Fire Fox on the Tiger machine because I can take full advantage of all of the features that it offers. It has a ton of add ons/modules if you like those kinds of things and I have much better success on certain websites than I do when I run Safari. Put simply, Safari just doesn't "play nice" with certain web sites that I have had to use over the years whether at home, work or for my son's college needs so I looked for an alternative browser early on.
Opera is a nice browser, but I like the Leopard version better and would recommend Fire Fox over Opera for that reason if you are running Tiger.
I would urge you to check out Fire Fox and Opera. See what they all have to offer and they are all free so you really have nothing to lose by trying them both.
http://www.mozilla.com/en-US/firefox/all-older.html
http://arc.opera.com/snapshot/mac/