|There is no finer smartphone display available today|
With the launch of the iPhone 6, DisplayMate has taken the (unsurprising) step of measuring screen performance and it's report makes for interesting reading.
The iPhone 6 Plus is rated as the best performing LCD display that DisplayMate have ever tested. That shouldn't be a surprise, as Apple has taken special care over the displays in its devices for decades, and every previous iPhone has performed well in this regard too.
What it didn't achieve, though, was to knock the Galaxy Note 4 off it's perch as the best smartphone display available. DisplayMate rated the performance of the Note 4's OLED screen as the best of any smartphone or tablet that they had ever tested. In particular Samsung's colour modes received high praise and DisplayMate suggested that this was something that should be implemented by every smartphone in future.
So if you're primarily concerned with display quality and accuracy it looks like you need a big phone, and if you want the best, then you want the Samsung Galaxy Note 4.