1: Comfort. Planar Magnetic headphones utilize huge magnetic arrays on either side of their diaphragm. The benefits are huge, including forceful bass and even articulation for low distortion, but the big downsize is comfort.
2: Sound Leakage. Unlike a conventional dynamic open headphone, which is open, but the diaphragm itself only projects sound one way--towards your ear, the sound leakage is minimal. With a planar magnetic, the diaphragm projects sound equally in both directions, meaning they're projecting the full brunt of their sound both towards your ear as well as out of the backs of the cans. Sound leakage is very apparent.
Outside of that, they don't really have much weaknesses. Being power hungry used to be a problem, but almost all of the recent planar magnetics are relatively efficient.
This, I was shocked with how loud the leakage is in comparison to my Shure 1840. I tried using just the outside and the sound quality is actually comparable to putting them on lol
Aswell, if it matters at all, impedance curves: