It's not so much the iPhone as it is the lower resolution of the streaming service combined with the lower resolution of bluetooth. Try a direct connection from the iPhone to your amp, using a 3.5mm to RCA adapter cable. Ditch the bluetooth. That will help, but Spotify is still relatively "low-res" compared to a CD.
Additionally, if you ever want to experiment with higher resolution from the iPhone, try ripping CDs as AIFF or ALAC (Apple Lossless) then sync it to your iPhone with iTunes. Then use an outboard DAC like the Audioquest Dragonfly series from your Lightning connector using a Lightning to USB adapter cable. 
I run my iPhone in the car with AIFF and ALAC files on it with the iPhone 'direct connected' to the car's DAC via Lightning to USB. This completely eliminates the iPhone's internal DAC and it's internal analog stage and audio quality is excellent.
In the photos below the iPhone is direct connected to the car's internal DAC, the cellphone amplifier & external antenna. The adapter also holds the iPhone securely in place. But even w/o the adapter you can see a USB port nearby. That port will do the same thing (except the iPhone will not be connected to the cellular RF amp and external antenna). The main point is to ditch bluetooth. A direct analog connection via 3.5mm to RCA adapter is better. A direct digital connection to an outboard DAC is best. In this case the outboard DAC is part of the car's audio system.
