I have a pretty souped up A1200 (68060@50, 128 MB ram) with OS3.9. Very nice machine, works like a charm. Browsing the web is almost unbearable, though. FTP, mail, IRC and stuff works great.
A completely maxed out A1200 is blown to pieces, speedwise, compared to the PIII/500 you mentioned. As you already know, Amigabrowsers are hardly comparable to their Windows & Linuxcounterparts. If you've never used a classic Amiga for surfing the web, you're in for a special treat...
I use my Amiga's (1200 & 3000) for the things they can handle easily. Browsing the web isn't one of them.