I didn't even know that was possible :o

Neither did I until recently. It can only do it in wired mode at present (Xbox One to PS4 that is) but they are working on wireless too. As I prefer wired though it works out great for me. Get too much wireless interference causing controller dropouts where I am... I have ended up spinning in a circle before now (was funny playing AC4 and standing on the dock spinning like crazy and not responding). It's not cheap but it means you can pretty much use any controller on any console.

Do the rumble features from the xbox one controller work when connected to the PS4 in this way?

Dunno yet... Haven't got my white PS4 because it's not out yet. Been playing with the reprogramming system though... and it is easy to remap ANY button to any other button. It uses a scripting system but you can use a gui to do it easier and it generates the script which is then compiled and dropped into one of 8 slots on the ChronusMax. This way you can use one layout for an FPS and another one for another game. You can even use a 360 controller on a 360... doesn't sound right does it? But you can remap the controls... One thing that pees me off with GTA5 is the flight controls... I'm probably going to make a script to shift the controls around and move the damned rudder to the right thumbstick. Putting the rudder on the bumpers is mental.