The Royal Hawaiian is a much more intimate property, not to say it's not bustling. BUt the SHeraton Waikiki is huge and FULL of people at all times. Don't expect any individual attention there.
The Royal's rooms are a bit tired, though generally large. I prefer the rooms in the original building, not the Tower, as the Tower has NO character.
The Sheraton Moana Surfrider is not too far away.....I like it ALOT better, and it's generally a bit cheaper than the Royal.
Aloha