Personally, I will go for flat screen smartphone anytime and any day. Flat screen, for me, is better choice for anyone that likes durability of phones. The edge flat screen devices have over slide screen devices are quite too enormous. There is absolutely no ground for comparison between the two different screen kinds of smartphones.
Prior to the advent of smartphone, those less sophisticated phones also came in either slide or flat slide. And I learnt my lesson way back then about the best screen between them both.
Without sounding too critical about the slide screen phones, they are very sleek and attractive to behold, but their disadvantages lie in their lack of durability, especially within the screen region. They are have what is called flexor, and this flexor enable them to slide from one end to the other. As this sliding is done continuously, this flexor would begin to wane, which would lead to the damage of it, thus unable to slide as it used to, which would also affect the screen.
But for flat screen phones, they can be used for a long time without the fear of the screen been damaged if carefully used.