I have an old model Braun epilator I've had for years and its the only thing I've ever used on my legs since I got it. One thing I notice is, if I go without epilating for a while , it hurts when I do it again but, if I just do little bits at a time and keep at it , it stops bothering me. Its like your body needs time to send out natural painkillers or something. I've actually managed to do my bikini line with it if I go in really slow short bursts. I've definitely never been able to stand doing even a hair or two of my armpits though. I don't have a model that's suitable for facial use so, I couldn't say about that.
Here's one thing I suspect could work that I learned when I had laser hair removal. If you get an ointment that's benzocaine or better still, lidocaine based in as high a strength as you can find, spread a layer on the part you want to depilate, wrap it in plastic wrap and wait (maximum anaesthetic effect usually hit around 45 minutes later),then wipe it off , it can diminish the pain quite a lot.
the numbness is pretty much gone after two hours.