Is this cabinet from Canada? The bottom one looks like the "Ontario Hydro Isolation Transformer" that Ontario (somewhat blindly) required in all their arcade games. This would not be original equipment.
The transformer with the Williams part number is probably original and looks like it provides low voltage AC for the game (logic, sound, etc.) in addition to probably an isolated line-voltage output for the monitor.
If you're converting to MAME or similar, it may be easier to use just the one in the bottom picture as then you won't have to worry about all the extra windings and finding the pinout.