A lot of dreamcast games were like this for the 5th generation of consoles. I can think of F1 Gran Prix and Rainbow Six as the examples that immediately come to mind, besides 2D fighters, which were always better on DC.
These ones are not really transitional, but say more about the power of mobile devices over time and Sony's jewishness, all of the PS3-Vita shared games and later Vita to PS4 ports. A decent part of PS4's library is shared with the vita, with it being graphical upgrades only most of the time. Digimon Cyber Sleuths, Gravity Rush, Danganropa, most of the Vanillaware games on vita, Tokyo Xanadu.
>>16901949
PS2 got a lot of those into the 7th generation, I can recall Sonic Unleashed and COD2 as well being other ones.