Prince of Persia came out in 1989, while Flashback arrived in 1992. In the late 80s and early 90s, pc video game tech was evolving at a breakneck pace, a 3-year gap was an eternity. Prince of Persia ran quite well on an 8-bit XT, Flashback needed a 16-bit 286. They are basically from a different era, and Flashback was surely inspired by PoP.

If you liked Flashback, try an earlier release (also from Delphine software) called Out of this World/Another World

Flashback had the bulk of Prince of Persia's mechanics but developed story and the puzzle aspect to a far greater extent and was less action based compared to Prince of Persia's race against the clock. There are times in Flashback when you have to race the clock but there are also times when you just have to stare at the screen and figure out how to do something or wander the world trying to figure out what you missed and where the fuck you are supposed to go next. Flashback is one of my favorites but I am not a gamer and the majority of my gaming was in the previous century.

Flashback came considerably later (1992) than PoP (1989); a single year back then was a lot more significant than it is today. A classic game in between was Another World (1991).

Just out curiosity, PoP ran on 8088/8086, while Flashback on 286/386.

It's more popular, especially with the subsequent games and media franchise. FWIW, I hear people talk about Flashback's predecessor, Another World, a lot. That is also a popular game.