Except the physical features are there any differences between the two races in the DC universe?
Because both White and Green Martians are shape-shifters, physical features are basically meaningless. The biggest different is that Green Martians are more peaceful and philosophical, while White Martians are born warriors and aggressors.
The White Martians' aggression drove them into a civil war against the peaceful Green Martians. Eventually the Green Martians prevailed and banished most of the surviving White Martians to a type of Phantom Zone (though apparently not the Phantom Zone). - DC Wikia
Because of their nature (and past actions) the White Martians are not viewed in a positive light.
A few exceptions include Miss Martian, who is a White Martian posing as a Green Martian.