Our standard calls for a foot more hare than cat like. Through the years of working with and having greyhounds I have seen many different foot types ranging from overarched to flat feet.
Flat foot prone to toe injuries
A hare foot is thought to be the strongest foot to hold up to running/turning. A hare foot has a slightly greater than 90 degree angle between P1 and P2.
Examples of a hare foot
A cat foot has a 90 degree angle between P1-P2. I personally have never had increased injuries from a foot like this but I prefer a hare foot.
The last foot type to mention is the overarched foot. The P1-P2 has a less than 90 degree. It would seem to be very punishing on the toes and luckily is an uncommon foot to find.
Overarched toes. This foot is less flexible and more prone to injuries.
No matter what type of foot the hound has, long toenails can increase the injuries. Keep those toenails short and take care of those hound feet!