Some sources (like TV Tropes and Pac-Man Wiki) say that Pac-Man Arrangement still has its two-player mode (albeit dummied out). Check if that's true.
Big sprites of Blinky and Inky. These originated from the credits screen of Pac-Man Arrangement (when it was featured in Namco Classic Collection Vol. 2), but this compilation skips the credits entirely for unknown reasons.
Pac-Mania has some debug-related text, including a sound test and a "3D TEST":
SOUND TEST VOICE NUMBER PSG NUMBER FM NUMBER AUDIO 3D TEST
Pac-Mania also has a disclaimer about international copyright:
THIS GAME IS FOR USE EXCLUSIVELY IN JAPAN. THE SALE, EXPORT, USE OR OPERATION OF THIS GAME OUTSIDE OF JAPAN MAY BE A VIOLATION OF INTERNATIONAL COPYRIGHT, TRADEMARK AND/OR OTHER RELATED LAWS SUBJECTING THE VIOLATOR TO LEGAL PENALTIES.
The Japanese title screen is missing "TM and" as well as "Licensed by Nintendo". The logo also has less shadow behind it.
Pac-Mania has a different logo in the Japanese version, based on the arcade original (along with being consistent with the logo seen after selecting the game). The US version's logo seems to be based on the one in the Genesis port, as there's no hole in the P.
The US version has tips, while the Japanese version has hints.