With millions of users and millions of web sites, there are always going to be issues of some kind, and most people do not take the time to complain about working things.
You do not know if they have a security packages installed that is interfering with their use of Safari, or if is a plug-in issue, etc... that those people are complaining about.
With respect to your version of Safari, it has not changed in a few years, but the web sites have been moving forwards using new tricks and features that your version of Safari is not keeping up with.
If Firefox works for you, as it is a current, up-to-date browser, that is perfectly acceptable. And if when you do get a newer OS X version, you still want to run Firefox, that is fine as well (Firefox is my primary browser, as it has extensions I find very useful at work and at home; but I also use Safari on El Capitan for some things and I do not have any problems with it).
NOTE: Your signature profile says "iMac, Mac OS X (10.3.9)", which is Panther and PowerPC only. You may want to update your forum profile 🙂