Why go all the way to Linux-equipped boards?

They represent very expensive ARM chips. And Linux is not an RTOS unless you run the real-time stuff below the Linux layer.

Next thing is that the Linux implementation most probably already have the required modules for the peripherials the chip supports. And modules for generic stuff are not ARM-specific so no need to have a library of modules written specific for the ARM - at least until you move to assembler. But even moving to the assembler, there will be some difference to the assembler depending on what ARM core that is used. Assembler for the smaller Cortex-M0 or M3 is using Thumb2 instructions where the instructions are processed as 16-bit entities, while older or larger ARM cores are using 32-bit ARM instructions or the older Thumb instruction set.

Anyway, the "normal" competitor/replacement for a 8051 chip is not an ARM chip with Linux but most probably a Cortex-M0 or Cortex-M3 with hands-on access to all peripherials and "emulated" single-bit instructions.