I should also mention that this is only on the iPhone, not re-sizing the browser or on my android test device. I think it has something to do with how BB is handling retina on the iPhone.
ps. I don’t think it’s a WordPress issue because both sites are running the latest WordPress (I know they did some stuff with image optimization in 4.4.x).
I think it is indeed an issue with the image optimization WP introduced in 4.4. I checked the original site and the image doesn’t have the srcset attribute added. You could try installing a plugin like WP Retina 2x to enhance images on retina display. Give it a shot and let us know how it goes!