Digital Camera VS iPhone 6

I am in my first year of painting, using photos exclusively as my source that were taken with my iPhone 6. As beautiful as the photos look on my phone, the printed out version is always less impressive -- the exposure, colors, values, are distorted. And I always have them printed at a reputable, professional print shop. 
So, I'm thinking of buying a digital camera, but my budget is limited -- in the $500 - $700 range. I'm thinking specifically of the Sony Alpha A6000.

I know next to nothing about cameras. My question is simple: Will a digital camera such as this one, in the low - middle range quality, produce significantly better printouts than photos taken by my iPhone 6? From the research I've done, it seems like a digital camera would be better but I'd rather not spend the money if the results would be similar.
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