With the FOX I found it was quite a bit slower - think it has less power, certainly less revs and a narrower power band. That's what it feels like to me.
I ended up reducing downforce slightly to compensate for this. Also the gear ratios needed changing too.
Think all cars peak power limits have been reduced in a similar way. Gear ratios will need changing. Maybe slightly closer gears or lower final drive.
The tyres are very different. In the FOX now the R1s are only good for a few laps with max pressure. I think this is what is costing the most time as you have to use R2s for anything more than a short sprint race.
The camber angles need amending too. In this thread I explain how I set up cars and in it is a useful way of finding the correct camber angles.
http://www.lfsforum.net/showthread.php?t=33099
If you've got less grip you are going to need a bit less diff lock too. This is another thing I have been adjusting since patch X.
Brakes too ofcourse. A bit less overall force maybe.
Suspension settings should be pretty much the same between X and Y with non-downforce cars I reckon. Minor adjustments might be needed to maintain a nice balance.
Have fun - making setups is a great skill to learn.