
The popular explanation is that people are more sensitive to differences within their own race. I'm not so sure. I think it has to do with exposure. The more you're around people of another race, the better you are at noticing the features that distinguish individuals.
Maurice Berger's book White Lies contains an essay by African American artist Renee Cox, who complains that white people often mistake her for Whoopi Goldberg, even though their only common feature is their braids. According to Cox, "I wouldn't be running down the street screaming...'Oh, that's Marilyn Monroe,' just because she's a blonde." Maybe not, but somebody recently wrote a letter to Parade Magazine claiming that Jenny McCarthy and Chelsea Handler "look like twins." Parade showed the following picture to compare:

The fact is that many people are just plain rotten at telling people of any race apart. The average person, when asked to describe someone, will usually talk in the broadest, most general terms. "She's a blonde." "He's tall, dark, and handsome." "She's got a big nose." My father was once talking to a friend at an Orthodox Jewish wedding and asked him to describe someone he'd seen. The friend said, without a trace of irony, "He's the guy with the beard and the dark suit."
I, a white guy, have had plenty of experiences where other whites have confused me for someone else. Whites may make these kinds of mistakes more often with blacks than with other whites, but it's a matter of degree. We needn't jump to the conclusion that it's always due to race.