I offer both of these treatments, so by default I have tried them. They are both great, although I personally prefer the perm as it's more low maintenance (from the client's point of view). Extensions look beautiful but they need regular infills, just like nail enhancements, and can look quite tatty when they need an infill. I also found myself needing to arrange them every morning, i.e. tweak them into place.
Neither treatment makes you look like a drag queen. A lash perm is very lifting for the eye area, it makes you look really fresh and awake. Lash extensions don't have to be really long, they can add volume, it depends what the client wants really.
Mascara can be worn, but for lash extensions it needs to be water based.
Both of these treatments are quite fiddly and need to be done well to look good