On pretty much any modern system, and the different Raspberry models are no exception, the OS doesn't really get in the way of programs that just do their own thing. The OS does matter a whole lot if you're shuffling files in the file system - that's a shared resource - but your process memory is yours and the OS doesn't get involved as long as you stay in that area.
Technically this is made possible by the MMU (Memory Management Unit) in the CPU. The OS configures it for your program, and then this hardware component just watches over your program to ensure you stay withing your memory space. The OS is only woken up by the MMU if you stray outside (the famous SegFault).
By far the fastest solution is to use all 4 cores of a model 2, including its VFP (Vector Floating point) unit. You'll need a modern compiler for that. The most modern compiler I can find for Risc OS is an older GCC 4.7, not the more up to date GCC 4.9/5.0 versions.
You'd also want to use an existing image processing library so you don't have to reinvent the wheel. OpenCV is the usual choice for the Pi, and it runs on Linux. You'd be hard-pressed to write your own code as efficiently.