An iPhone 6 is as good, and in some ways better, than your typical budget point and shoot cameras. (those under around $200). What you lose in zoom, you gain in touch screen, easy social media sharing, in-camera editing ability (through the native functions and countless apps), gps tagging, etc. So compared to a typical sub-$200ish P&S, you are losing zoom, gaining some extra features, and basically matching image quality. (Though particularly the large iPhone 6, has image quality better than some P&S cameras).
If you want better image quality, then you most of those cameras don't fit in your pocket. There are some premium enthusiast cameras, like the Sony RX100, that can deliver high image quality, yet remain very compact.