There's been a fair bit of effort to get RISC OS software working on ROOL's port of RISC OS to the Beagleboard and other OMAP-driven boards. The shift from software that works on the Iyonix to software that works on the OMAP family isn't as big as the shift to 32-bit of a few years ago, but there are still some issues. Most importantly, the OMAP family of processors use the 'ARMv7' specification, which means that certain instructions that work on the Iyonix's IOP processor (or earlier) fall over.
The ease of fixing a recalcitrant application depends on how it's been written. If the app's written in BASIC, then all should be well. If it's written in C, then a recompile with the latest version of the GCC or Norcroft tools should fix it. If you've got some hand-crafted assembler to cope with, then the process is a bit more involved. There's a full list of these technical issues here.
As time goes on, more and more software is having fixes applied to enable compatibility. Over the last few days, David Pilling's Ovation Pro and SparkFS have been updated to work with the new hardware. The text editor Zap has also been fixed, though there's not an official release of this yet. Apps like NetSurf, KinoAMP, ArtWorks and RDPClient already work, and there's some indication that EasiWriter and TechWriter will soon join the list.
More details on the applications that work on the new hardware platform can be found here. Hopefully this list will keep on growing. Meanwhile, at least one RISC OS user is happy with the experience of using the BeagleBoard...