I've got a Nikon P100 and it's zoom kills my 1020. There's simply no way the 1020 can compete in that regard with any half decent camera. But if Zoom is not used or not necessary? 1020 all the way. It produces just so much more detail and I really dig the vibrant colours (though I can understand why some people would complain about them. I do hope Nokia will update this in the future so you can choose). Another advantage is that it's just much easier to use, the interface is quick and you obviously have more possibilities thanks to various apps.
I can't really imagine some of the low-end P&S (i.e. sub 100, 150$) competing with the 1020. But anyway, if you are really looking for a proper camera and that's your primary motivation, you shouldn't go with the 1020. As good as it is against entry and mid-level P&S, for the same price you can get a decent DSLR and maybe a good set of lenses, too. That will definitely give you better pictures, if you don't mind carrying it around.
EDIT: Had a couple more thoughts flying around. For night time shoots, I feel that a decent P&S might still oust the 1020. My P100 for example can go as high as 8 seconds for exposure. On the other hand I genuinely doubt that most P&S can do decent video, especially with audio filtering and such. My P&S does 1080 at 30fps but the image quality is not really notable, there's no optical stabilisation so you get a lot of shaking and using an optical zoom in video has one big disadvanage: it gets LOUD! The 1020 zoom is not really audible since it's all digital, but optical zoom involves moving parts and since they are directly connected to the body of the camera, you can be sure to hear them afterwards.