AWeb, if I recall, comes with OS3.9, but it's an older version, and I think one of the official boing bags had an update for it (official boing bags meaning 1&2).
There is a rather broken version of OWB for m68k I've tried at one point, and it was horribly unstable. Netsurf really is the best 'modern' browser for the Amiga 68k. I've noticed that it seems a lot slower than it is, because it waits to show anything before it's rendered. The trick most browsers do to make them seem faster is to start showing things as they're loaded, but netsurf doesn't do that, it waits the 5-15 seconds (for me) to then show the page is loaded, but it loads the whole thing.
It actually is fairly fast, though I'm running it on a 060/50, with tons of ram (well, in Amiga terms, I have 380mb~ of fast ram.)
For most day to day use though, I use IBrowse, 'cause it actually works while doing other things.
slaapliedje