I think three thing that tell that Mesopotamia was advanced was their achievements, art/ architecture, and system of writing.
Mesopotamia had tons of achievements such as : the wheel, the first set of written laws, had advanced trade, first use and creation of medicine, etc. I think Mesopotamia's achievements show that they were more advanced because, they had to be talented to be able to create and build stuff. Also if they hadn't created the stuff that they had then they wouldn't be able to get well with the use of the medicine, the wheel for transportation and farming, the first set of written laws for telling the citizens whats right and whats wrong, etc. They invented those wonderful things for them but they also benefit us.
System of Writing
Mesopotamia created the first set of written laws called cuneiform. Cuneiform is what they used back around 3500bc. Mesopotamia created Cuneiform for keeping track of how much supplies they had such as: wheat, grain, etc. If Mesopotamia hadn't invented cuneiform then we might not have a way to communicate. If Mesopotamia wasn't advanced then they couldn't have created cuneiform.(Click here for more info)
Mesopotamia's architecture helps them create homes, shops, etc. Mesopotamia had to practice building homes and shops. If they hadn't practiced then if a storm or something comes then it might hurt the people. Mesopotamias art is very important to our generation. Its important because we can learn about their different lifestyles.