Elvis was famous because he was something new. He was one of the first big stars to come from the rockabilly movement of the 50s and people instantly fell in love when they heard his first record, That's Alright Mama (which was actually a cover). He had fans from all ages all over the country. Next to his music Elvis also caused an uproar with his hip movements, which were unprecedented, and contributed to his popularity.
I'm not a fan of Bieber (although if Boyfriend came on the radio I probably wouldn't turn it off :P), and from what I've heard he doesn't really exemplify any of these qualities very well. Does he have what it takes to be an even bigger success? Yes. Is he comparable to Elvis? Not in a musical context. Popularity though? Maybe.