I much prefer dragons. I only know about green iguanas, and all mine were rescues, so that might color my opinion of them.
Iguanas are great when they're tame, but it takes a lot of work to get them that way. They get much larger, up to 6 feet in length, so they will need significantly more space than a dragon. Iguanas are kind like dogs. You have to learn to become the alpha, a lot of socialization, make sure they get plenty of exercise, and read their behavioral cues in order to end with that cool lizard that will hang out with ya all day.
Iguanas are more sensitive to stress and their environment. They might react to little things like hats, the color of your clothes, etc. They might act differently during breeding season, or to women's cycles. Males are most known for this, but I had a female who became aggressive towards me during breeding season as well.
Here's a link that gets into care and the good and ugly sides of owning an iguana.
http://www.anapsid.org/iguana/index.html
Honestly I would advice against getting an iguana unless your experienced with herps. I do not consider them to be a starter pet. I wish it was illegal for pet stores to sell them. Many have no idea what they're getting themselves into, and the result is a lot of abandoned animals. many rescue centers are filled to capacity with iguanas and have to turn them away. Don't get me wrong, I love iguanas, but they they can be difficult to care for, and even harder for a rescuer to clean up the mess after improper care.