OK, sorry, sorry, sorry, my previous post was somehow inaccurate. Here's what really works on the iPhone 6 (at least), to get the caller's picture at full screen size. The height of the picture must be at least 960 pixels, and the width at least 640 pixels. The picture can be resized in Contacts with the slider without consequences on the full screen display, but be aware that if you move it within the frame the actual size can change and thus reduce a dimension below the required threshold.
What is still exact from my previous post though, is that to get a large picture when tapping the contact's image on the iPhone, the width of the picture must be at least 282 pixels.