I personally have repaired many of these board sets of both vendors. I own a midway space invaders and a few TAITO Space invaders board sets.
The differences arise through the licensing agreement. TAITO owns the rights to Space Invaders and then MIDWAY purchased the licensing for North America.
The licensing (Along with much much more) said that Midway had to develop their own hardware. The MIDWAY version board is a black & White only board set and they used a green/Yellow/red vinyl plastic to give the illusion of color for the top/middle/bottom areas of game screen. MIDWAY also used two buttons for left & right.
TAITO, (The owner) made their board to support either Black & White, or on board color. The Controller it either buttons, or a left/right joystick.
Comparing both schematics, you can see many areas where the circuitry is the same, sometimes one chip is turned into a few chips. But this is how MIDWAY duplicated without infringing on the licensing.
As far as repairing, I prefer working on the MIDWAY "L" board. those 6 ribbon cables on the TAITO can be a pain.
The EPROM's can be different values and there are STRAPPING jumpers to connect for the proper EPROM type that you have. These EPROM's are getting harder to find so sometimes you need to swap in a different type to get it working.