Supposedly paper filter is healthier because it filters out the cafestol
For me the biggest problem is the washing... but coffee tastes better this way.
I use a silicone spatula to clear most of whats in there into a compost bin. I drink a lot of coffee so it's still a _little_ cumbersome but it definitely helps the process a lot.
I have an Aeropress and the vast majority of time the cleanup is just pushing the plunger the rest of the way in, which pops out 99% of the grinds and the filter, and then you just rinse off the end of the plunger under a faucet, and it's clean. Extremely low maintenance, would recommend.
Yeah I have one at home and like it a lot. Still, it's plastic. Wish you could get one in pyrex or stainless.
There's some murmurings that Aeropress is planning to release a "Premium" model made of glass + stainless. Don't think there's any official web announcement to link to; think the new models were demo'ed at an expo or something.