I've done some research into this and my conclusion is that it's mainly down to the X68000 having the same CPU (a Motorola 68000) as the CP system (which used an encrypted but otherwise identical variant), and the powerful but not equivalent graphics of the workstation.
Having the same CPU meant that it was possible to rapidly prototype and debug code on the X68000. As well as having access to all the debugging tools available for the X68000, it's almost always faster to test code directly on the development machine than it is to have to download it to some kind of ROM emulator attached to an arcade system board.
During development of games, it is often necessary to rapidly iterate and experiment with various parameters. Tuning the game to be fun, challenging and profitable is a major part of the development process. Being able to do that quickly on the X68000 would have been of great benefit to Capcom.
The graphical capabilities of the X68000 were impressive for the time, but not as powerful as the CP System. However, they were good enough that gameplay elements could be tested, running at the same frame rate as the arcade system, and looking close to the finished project. Indeed, the X68000 had near arcade perfect ports of many CP System games.
Specifically, the X68000 supported 16 bit colour, where as the CPS supported 32 bit. However, conversion between them can be done automatically by software, and is trivial. Colour limits on sprites and tiles are similar on both systems.
Additionally, both systems have similar sprite capabilities, using 16x16 sprites. Many CPS games used multiple sprites to create bigger objects, so by having similar capabilities code to handle that could be mostly the same on both systems.
To make all that possible, Capcom would have had to write separate code for low level X68000 and CPS graphics, but once done the same code base could be used for both systems. This is common nowadays with things like a portable RTOS (embedded operating system) and standard code libraries that allow the same code to run in a test environment on a PC, and on the target hardware.