We usually eat at both every trip and enjoy both. Palm is more upscale and expensive, great if you are looking for steak and lobster. Kitchen is more relaxed and casual, but food is very good. I would suggest looking over both menus and decide what appeals to you most. I think you will enjoy either. Have a great time!
I enjoy both restaurants but I would probably choose the Kitchen. I'm in a more casual mode on vacation and there are a bunch of nice steakhouses near where I live including a couple of Palm Restaurants.