In brief, MorphOS is said to currently have the best integration of it's 68k emulation and compatibility in running legacy software. AOS4 is close behind and to my knowledge (which is very limited when it comes to AROS) the 68k emulation for AROS is not been done yet and they are now thinking of using WinUAE in AROS to run old Amiga software.
You can try MorphOS for classic Amiga computers for free if you have a CyberStormPPC or BlizzardPPC card in one of your classic Amigas, and for the past few months AmigaOS4.0 for Classic Amigas with PPC accelerators has been available for purchase.
So, if you have the "Big Bucks" and can find a PPC card for your A1200 or A4000, or you already have one, you could upgrade to a PPC Amiga like OS and give it a test drive.