Made it to level 4 last night. I had about 20 hrs on the PS4 beta last week and I can honestly say the two play exactly the same. Load times seemed equal.The PS4 look slightly better, but I believe that is due to the XB1 beta being 720p vs PS4 being 1080p. That is supposed to be leveled out by release time. In the PS4 thread, they are commenting about how the PS3 vs PS4 graphics are very similar, so we have to remember that the visuals are turned down to accomodate the lowest common denominator, which is the last gen systems. I dont think we should be expecting major differences between versions, a la COD/BF4. I think if anything you should be choosing the platform where your friends are and the place with the most stable online component.
Since I had a buddy playing with me, we decided to do the Hard mission for Level 3 story. Big mistake unless you have some shotguns, we both had snipers. The Wizard part was killing us. Switched to Normal and breezed right through. Hoping to get to L6 to open up Crucible tonight and really see how XBL matchmaking factors into better opponents, faster times between rounds, etc. I was getting destroyed by good players on the PS4 side.