Internet explorer is worse than BeIE in some ways and better in others. Overall it's about as lousy.
On plus side you can set it up to open files you click in file browser. It does not do that by default in BeShell; let me tell you the secret of getting it to work: run Tweak program (in Utilities folder), go to file types tab and find html files. By default, it will say BeIE.exe %1. You will want to change it to Internet file://%1. Note that this same trick will not work with BeIE (at least with my version, which seems to be the latest of BeShell).
Note that BAS BeShell was supposed to fix many things in BeShell so it may have fixed this, too.
Note that the biggest problem with either BeIE or Internet is that it can't turn the screen sideways. You're stuck with on-end orientation. For many pages that's not too bad, but for most forums and pages with code in them, this means you have to scroll sideways all the time.
On the plus side, with Internet you can scroll using cursor button - with BeIE you have to use stylus to scroll.