OS4 is a continued development of the Amiga operating system you used to run on your Commodore Amigas. Parts of it have been replaced, and it now runs on PowerPC natively. It runs system friendly 68k apps directly, so 68k and PowerPC processes run side by side. This has the advantage that when a 68k program calls a system library, the system library is native PPC code, so it runs very fast indeed. Anything which uses the old Amiga chipset directly has to go through UAE. OS4 comes with a full version of AmigaOS 3.1 and a tool called RunInUAE to help make that seemless.
AROS is an open source reimplementation of OS3.1, although it has been extended beyond that original goal. Most system friendly Amiga software can be recompiled for AROS if you have the source code. It does not run 68k apps as if they were native, it can only run 68k apps through UAE (although JanusUAE tries to hide the UAE backend and make apps look native, with some success). Historically it was always far behind AmigaOS 4 and MorphOS, although it has made some good progress in recent years.
MorphOS is another clone like AROS, except it is commercial and closed source (although it shares some sources with AROS). Like OS4, it also runs only on PowerPC, and it also can run system-friendly 68k Amiga software as if it were native.
My personal preference is OS4.
