Both David Bailey and Annie Leibovitz are very good portrait photographers. But I think her style is quite different, very meticulously arranged and composed.
Bailey's style is more relaxed. Apparently, he spends much more time chatting and drinking tea with his subject, than actually photographing them. A great technique to make people feel relaxed and open up to the camera.
He also likes to crack jokes on the cruder end of the scale. Who knows what he said to make the Queen laugh?