Kaygela--if you can fit them both in time wise and budget wise going to both would be great. Then you can field this question next time it comes along.
We did have a reservation for Tchoup Chop but did not have one for The Kitchen. Since we were staying at HRH, we just stopped by The Kitchen on our way in from the parks and put our name in. I think the wait was about 45 minutes. We had the "your table is ready" flashing/vibrating device and were able to go back to our room to freshen up and get a drink at the Beach Club before our table was ready. This worked out well for us because we don't like to have too many reservations when we are on vacation.