I think the Prince of Persia revival mechanism is a whipping boy for its generally low difficulty. You will note several reviews still state that it is frustrating to have to repeat a particularly long sequence of platforming regardless of the save, and the Wings of Ormahzd is a particularly frustrating mechanic.
Frustration at Mirror's Edge seems more angled towards the fact that despite being urged to avoid enemies wherever possible, the game throws segments where you are told you must engage enemies to continue, something Faith is deliberately designed to be poor at. That several of these segments are in fact avoidable does not excuse the mixed signal; many players still engage those enemies on first playthrough, and being killed over and over due to the relatively high difficulty of timing disarms or defeating multiple enemies is a common complaint.
I think the major difference in terms of difficulty, as well as the source of claims that PoP's game mechanics amount to 'excessive hand-holding' comes from the difference in control. Ironically, while many people were skeptical of Mirror's ability to handle platforming in a 1st, rather than 3rd person perspective, the end result is a capable platformer with intuitive controls. Prince of Persia takes a 3rd person perspective, and then automates a lot of the movement so that it is rare that the player will be off angle or off time on any jump. You can perform a string of movements which would require intense concentration in Mirror's Edge to perform by sitting back and pressing the jump key on Prince of Persia.
It's not because you get rescued that the player's sense of achievement is lulled in Prince of Persia. It's because whilst playing it you have an eerie sensation that the game is responsible for most of the cool stuff you're doing. It's similar to Assassin's Creed's "Hold this button down to be awesome" system, only more automated.