I did the big cat feeding experience at Paradise Park a few years ago with my brother for his birthday.
It was really good and the guy who was with us was really friendly and informative.
As I recall we fed some tigers (through bars), cleaned out an empty tiger cage including shovelling poo and cleaning away empty bones from dinner, got taken round to see lots of other types of big cat. They then offered us a chance to walk into the cheetah enclosure to hand feed them. At the time they didn't advertise this but added it in if guests had been reliable and well behaved up to then (sounds patronising but I think they just wanted to check you would follow instruction and keep calm).
We did that, chaperoned by two keepers on either side of us and the cheetahs were amazing. They came up and ate out of a small bucket we held.
On the way out the enclosure my 6ft+ brother, who is normally as a cool as any cat, fainted and jammed the doors open as he fell to the ground. The keepers with us called for help and within seconds we were surrounded by a sea of green uniforms 
.
The cheetahs had long since scarpered to the other side of their field - not wanting to hang about if humans were going to be acting weird.
Everyone was very sweet and made him tea and sandwiches when he came round. In retrospect I think he'd just been a bit under the weather and not eaten/drunk enough up to that point in the day.