Pro mode allows you to set up your camera to your preferences.
Most of what you get with the iphone and especially the pixel is the post processing the software does.
With the iphone it's warmer colours and pixel is upping the HDR and sharpening
Personally I'd recommend capturing in RAW or using Expert RAW.
Setting manual settings for the particular image you want
Then editing afterwards
The results are almost always better.
Obviously takes practice, but I'm long run will get better photos