We can't have modern browser with all features, just not possible. Netsurf would be nearest thing to that.
Could be that Netsurf would be the best option. But there is no way "around" the increasing complexity of normal, "every-day" websites and the HW requirements in order to display them properly, though.
I kind of admire any effort to update the "browsing experience" on classic Amigas. It has some nerdy kind of coolness over it that I like. Taking the HW way past what people commonly thinks would be possible. And that was my point of bringing up web browsing on the C64 above, I never meant to say that Amiga classic HW and the C64 HW would be the same or has the same capabilities, or anything like that.
But no browser on any classic Amiga can bring you a *proper* (read: *seriously useful*) browsing experience today. The penalties, compromises and sacrifices will be too big to make it meaningful. It won't come close. So what's the point, really? I mean, other than the "geek factor"? If you want to browse Aminet from your classic Amiga, you can do that already from IBrowse. You want more? Well, with some work, you could indeed get some more. But you could never get as far as to 2012. You would miss it by a decade. Or thereabout.
The C64, and the classic Amiga HW, is really cool HW. I have 3 C64's, 1 C128, 2 A1200 and 1 A600. They are in my garage, but sometimes I dream of rigging them up and spend a couple of days going through all the disks, all the games, read all the magazines I have saved, etc. Someday I know I will do that, just haven't had enough time yet. But they are museum objects, retro gear, and I would never use them to "surf the web" in 2012. It would be for retro reasons alone.
I like the Amiga environment though, and I always fancied the idea of having an Amiga with modern capabilities. I think my MorphOS MacMini fully qualifies there. And
Odyssey (not "MUI-OWB", quit saying that please) actually does a better job with HTML5/CSS3 than Microsoft's latest publicly available version of Internet Explorer, and it outperforms Firefox by a magnitude, and it does it in a true IBrowse fassion.
That I like!

