I've got a green nylon one to match my green cordura saddle.
I love it. My first horse had issues with catching that were never really resolved. He'd be a gem at home, but if he ever got loose in a more stressful, non-home environment,(thank God that only happened once, and it was an enclosed area) catching involved a lengthy process. So, switching halters for bridles and vice-versa was a tricky and risky process. It was a lot less stressful to just trailer him to the trailhead in the halter part, and slip the bit in without taking all the headgear off and risking a loose horse.
I haven't found a downside to them - I've found mine incredibly handy. I want to buy another eggbutt with a copper mouth and set it up permanently for Scout, rather than constantly swapping bits around.