To me ranked is more fun than normals. You get a better level of competition and it is a way to test your mettle and skills. On top of that I find it nice that it keeps track of your statistics so you can see your progress.
The advantage of normals however is that it is laid back. You have a chance to test new builds and champions without fear of getting absolutely crushed. After you get a feel for it however you still won't be able to see the viability until you test them out in a more competitive environment.
Another positive to ranked is that you start to get to see the same people and it is easier to make friends imo.
To the person who doesn't like mirror matchups, there is also a draft mode for normals.
If you are ever on tilt in ranked you can always rest in normal games. They are both fun.