We are looking at getting one of these for my DD who is 12. Basically, either brand of tablet/e-reader does three things:
--functions as an e-reader
--allows the user to download apps and use them
--allows internet access
Most kids will use one of these as a hand-held gaming device. So they are both exactly as kid-friendly as the games/content your child downloads. You are putting the internet at your child's fingertips on a portable device.
In my house, managing screen time is a significant challenge. We watch no TV, but my kids each have a Nintendo DS, we have a Wii and a PS3, we have a computer and a laptop. Other than Nintendo DS, we don't allow our 8 year old to use any of these in his room. Our 12 y/o can use the laptop in her room with permission for homework and to check email. Neither my H nor I have smart phones. Even without TV and smart phones, we still feel like our kids spend a lot of time in front of a screen.
At this point, we are leaning away from Kindle Fire and toward a plain Kindle e-reader for our 12 y/o. My 8 y/o son would love having access to Angry Birds, but he doesn't need yet ANOTHER way to play video games.
If you are just looking for a kid-friendly device for your child to play games on, maybe consider a Nintendo DS. Cheaper and without as much internet access.