I get eye strain from watching LED-based display (due to PWM), and also due to intel graphics driver. But if I look at LCD/CCFL display screen, I look at it for hours non-stop without any eye strain. The problem is many display screen is now using LED including phones.
I have tried many different phones like Samsung, LG, Huawei, Lenovo and all of them give me eye strain. I have purchased phones, only to get eye strain, and had to sell it again (at a slight loss).
So far, the only phones that I can use without eye strain are phones that uses the Super LCD3 display (i.e. HTC One M7, One Max, HTC One M8, M9 and M9+). These are the phones that I can use and look at the screen for hours (e.g. watching youtube or movies on my phone) without any eye strain whatsoever.
Other display technology like SuperAmoled (Samsung phones), IPS (LG, Huawei, Lenovo etc) all give me eye strain. Some newer HTC phones are starting to use IPS like the HTC Desire Eye, HTC E9+ etc, these also cause me eye strain, so not all HTC phones are okay, only their flagship series (M8, M9, M9+).
You should give HTC One M8 or M9 a try, and see if you get eye strain or not.