I'll just go out on a limb to generally say that a G3 is by no means fast enough to render modern web sites. If you throw enough RAM, OS X or Linux, and a modern release of Firefox, Webkit, or Chrome at one, it would do it, but it would be very angry at you for it.
I have Pentium M systems, which you'll recall are known for roundly whupping the ass of Pentium 4 back in the day. Those Pentium M systems are all faster than a 1.8GHz P4M I had back in the day, which
itself performs approximately as well as the 1.67GHz DSLD PowerBook G4 at Cinebench. (Making this an extreme approximation, but:
If you take the thought process that "A G4 is just a G3 but with altivec" than a 1.67 G4 should be3 at least 150% the overall speed of an improbably fast G3, say a blue-and-white with a 1GHz upgrade, or one of the fastest G3 iBooks.
Now, back to the Pentium Ms. Those things
barely render web pages. It is in all senses a waiting game with a machine like that to go on, say, npr.org or apple.com or theverge.com and let the page render. And, those are machines that support up to 2 gigs of RAM and run Windows 7 and current web browsers, so you have a relatively apples-to-apples comparison with modern computers.
Now, if your point here is that this is all somehow morally or intellectually "wrong" in that web pages that render poorly on even Pentium Ms is something devs shouldn't do, then yes, I agree. I'd love to be able to still browse the web on my Pentium Ms and my Atom netbooks and early Core2 machines.
If your point is that the machines "can do it' even though it's basically provable that they can't acceptably do this task, or that the web is somehow different in nature than we know it to be, then, I'm sorry, but you have been misinformed.
It is not an old mindset, it is a different one. The fact is that there are competing views and always have been. This mainframe+terminals vs local computing resource. I wasn't around then, but the parallels are clear. There is nothing I can do for people who are stupid and continue to shoehorn things into a tool primarily designed to retrieve and display HTML pages. They are wasting a lot of time trying to shape a stick into a pickax/shovel/sword/... combo-item. Eventually they are going to have to ditch that approach for a different one; HTTP is not a good way to make a remote application.
The flash is the problem mindset is an old one. I'd put money on every animated ad you see on the web these days, or 99.something percent of them, being animated with HTML5 and CSS and javascript - mostly to be able to show ads to iPhone and iPad users.
To add, "HTTP as a way to deliver applications" has actually worked fairly well. Is it a good use of local resources? No, not really, but those resources are cheap, people accept it as a valid alternative, and computers are fast enough to make up the difference, so developers keep doing it. Plus, this is literally how ChromeOS works and Chromebooks are currently the most popular type of laptop sold by the world's biggest retailer, so it's not like this is some kind of fluke.
I don't know if, at this point, there's any way to make them stop.
But that's not even what's being discussed here. At the core of what the OP wants is things like the web site to their local NPR station, CNN, and eBay. Those web sites are massively heavy and take a lot of resources to load. That's the kind of thing - modern HTML pages built with modern HTML techniques, that tenfourfox is okay at but G4s and G5s really aren't, let alone classilla, which is essentially code from the early 2000s, which as TheWhiteFalcon says, is itself held back by the fact that OS 9 was never afirst-class platform for Mozilla. I think WaMCoM Mozilla only ever really existed on Macs because it was still easy to port to Macs from when it was basically split off or continued on from a late release of Netscape.
It's not really
only the fault of something like Mac OS 9 not supporting the G4 well. The G3 is a 20-year-old chip at this point, and the G4/G5 were slow compared to Intel platforms even in their time. I think on a relatively well equipped 7+ system you could hypothetically write a "modern" browser, although it would be such an extreme amount of work I don't think that anybody who "could" ever will, and that anybody not already skilled at both writing web browsers and programming for system 7/8/9 ever will. My thought process here is that Classilla, which is really wamcom Mozilla cleaned up a little bit with a new icon and name, is "good" but it hasn't moved the state of the art forward on that platform from where it was fifteen to seventeen years ago. Ultimately though, a G4 running OS 9, any version, is going to run code at a certain speed.
The problem the OP is having is two-fold:
1) the browser they have (and there will NEVER be a significantly better one for OS9) can not handle the complexity of modern javascript.
2) The computer they have, even if they used a better OS and browser, will slow down a lot under the load of modern javascript, because web sites have overly large amounts of it that is very complicated.
We can agree all day long that web sites shouldn't do that, but they will not stop, so the only real solution to OP's problem is to find a faster computer. Switching to OSX in the mean time is a Band-Aid which
might help the computer not crash while rendering a page. It will not make anything faster,
and if it's a slow enough G4 it could slow everyday usage down a lot.
G4s were not great at the web in 2005. They are downright
awful at it today. Most of the G5s aren't really that much better. I will personally (as ever) make the argument that it's not really the best use of anyone's time to try to make a G4 their daily driver. A G5 is closer to that line, but it does not cross it.
(The line is Core2, by the way. A well equipped 45nm Core2 system is noticeably slow, but you can equip them with 4-16 gigs of RAM, depending on the particulars, and a good GPU that Chrome might be able to use to help rendering or accelerate display, etc.)