Samsung Galaxy S6: 5.1-inch, QHD '2K' Super AMOLED, 577ppi, 536 nits brightness
iPhone 6: 4.7-inch, 1334 x 750 IPS LCD, 326 ppi, 504 nits brightness
Size is the first big difference when comparing screens. The S6 packing a significantly larger screen, which means more room for enjoying your videos and browsing the web.
The next is resolution. The S6 also benefits from the same resolution upgrade as the Note 4 and as a result is sharper than the iPhone 6's display. There's still a debate about how useful 2K displays are on a small screen and most will probably not appreciate the differences. If your desperate for cutting-edge tech then the S6 is the winner here. Unless you look very closely, though, you won't notice the difference in sharpness.
There's differences in the display technologies as well, and these have a bigger impact. While Apple uses LCD, Samsung opts for OLED and as a result the S6 delivers perfect black levels and impressive contrast ratio that make it more suitable for watching films. The slightly over saturated colours you get with the S5 is not as problematic this time round on the S6, particularly when you choose a more tasteful colour setting. The iPhone 6 on the other hand delivers strong viewing angles and good colour accuracy.
So yes, the iPhone 6 has a great screen, but the S6 is offering something new and innovative with its 2K display and wins this round.