Essentially, it means the same thing: Currently the phone is not usable. However, when does imply permanence. Like does that car work? No that car doesn't work. In that instance, the car just doesn't work, it's broken, it has not worked for a long time, and will probably not ever. Or if you get a box of light bulbs and one "doesn't work" it means it's broken in a kind of permanent way. Whereas the phone is not working, almost reads like CURRENTLY the phone is not working. Or RIGHT NOW we are having problems with the phone. It implies the phone has stopped working recently and people are working to get it fixed. The INTERNET is not working (OKAY, LET's just wait for it to come back on). This computer doesn't work. (OKAY let's buy a new one). I would use the first one and add a word like currently, or at the moment, to imply that it is a temporary problem and people are working to fix it.

The phone is not working right now, it is broken.