There are laws of physics one cannot simply work around. Smart phone camera will never be able to compare with same era premium compact, CSC or dSLR.
Smart phone camera has evolved to the point where it is good enough for daily Social Media mug shots but personally I think they are a long way off if you serious into Photography.
Premium compact from Canon (G Series), Sony (RX Series) and Panasonic (LX Series) are good options if you want pocket ability. The premium compact will easily blow away a top of the range smart phone camera.
A step up from premium compacts are CSC from Olympus, Sony, Canon and Panasonic. The Olympus PEN series is definitively worth a look but there are lot of other options.