At launch? No. The first 2 years games will probably be nearly identical with PS4 versions running just a bit smoother.
After that though yes. As next gen engines really start to get optimized and devs become famikiar there will be a clear difference. The gap in power this gen is much larger than the PS3/360 gap.
That being said in terms of features games will be identical as the consoles are close enough that the gap wont generally effect gameplay (with the exception of frame rate).
Basically think of the X1 as Med settings and PS4 as High.







