Yep, as you have discovered the CE browser is a cut down version of IE and missing many components. You can get flash and PDF viewers but these are sold as additional software, not free. (Wyse buys these in from third parties)
If you want a Kiosk for general Internet access with all the functionality unfortunately you will need IE on XPe. If you can live with reduced functionality the suggestion of RDP to a Mozilla app could be great or buy the flash/PDF viewers for CE.