What's the difference between a cur and a hound?

For the strict definitions:

http://www.dictionary.com/browse/cur?s=t

cur
1. a mongrel dog, especially a worthless or unfriendly one
2. a mean cowardly person

http://www.dictionary.com/browse/hound?s=t

hound
1. one of any of several breeds of dogs trained to pursue game either by sight or by scent, especially one with a long face and large drooping ears.
2. Informal. any dog.
3. a mean, despicable person.

For the canine versions, a hound is a group of specific dog breeds while a cur is basically a mean mutt.

For the human versions, a cur is a coward but the hound is merely despised but not necessarily a coward.

This definition is basically correct, but there is a distinctly American usage for the term "cur" that refers to certain mixed-breed (but bred, not random mongrels) hunting dogs used for treeing prey, such as the catahoula cur (aka the catahoula leopard dog, which I presume prompted this question).

Dogs which would naturally tree quarry, regardless of ancestry, were discovered, favoured, and bred [by North Americans] out of necessity, but as these contained non-pedigree, unknown, or non-European bloodlines, they were looked down upon by dog experts of the time and given the name curs.

https://en.wikipedia.org/wiki/Cur

True European hounds of the time would lose or abandon treed prey, because they were brought up to hunt ground animals (rabbit, fox, deer). But many North American prey animals lived in forested areas and were avid climbers. So the true difference between hounds and curs were whether they would pursue and stay with treed prey, ranging from raccoons to bobcats to possums to bears.

However, some hounds were then interbred with curs to develop, for example, coonhounds such as the Treeing Walker Coonhound, which are called "hounds" but are recognized as hunting dogs, the same as curs. Thus, in this North American usage of "hound" and "cur", the difference is mostly historical.