Peace be unto you.
It is clear that you are not a Muslim, and - from the tone you used in posing your question - you might even be a little bit hostile to Islam and to Muslims. I wonder if that hostility is going to render you unable to give my answer a fair hearing. Allah knows best.
I entrust this affair to Allah as I offer you my answer to your question....
"Allah akbar" means "Allah is Greater." We Muslims know that saying as the "takbir", which means to affirm greatness.
"Allah is Greater" IS a comparative statement, but not in the way you presumed in your question. We are not affirming the Allah is Greater than other gods. The bedrock principle of Islam is "laa ilaaha ill-Allah" = there is no God in existence except Allah. So it's not possibl that we are comparing Allah to another god.
When we say, "Allah is Greater", we are saying that He is greater than anything and everything in Creation, AS WELL AS any experience (good or bad) that we may enjoy or be suffering from in Life.
In the Qur'an we are taught that the things of this current world (called "the Dunyaa") are ghuroor. The word ghuroor means illusion. "...for the life of this current world is but goods and chattels of ghuroor." Qur'an 3:185. There is a reason I'm saying this. Please bear with me.
The illusions of this world - money, fame, material goods, even our poverty and suffering - all these thing trick us into believing they are big deals. People crave wealth and an easy life. Most people do. We scheme about getting it. We spend huge amounts of time chasing after it. Those who get it worry over it. They worry that someone might steal it or cheat them out of it, so they concern themselves with protecting it. And all this SEEMS like a big deal. To most of mankind, these are great and weighty matters. We get so caught up in dealing with all these worldly cares that we begin to neglect our relationship with Allah and we neglect to make any serious effort to prepare for the Day of Judgment. This is a serious problem for a Muslim.
We Muslims are taught to affirm Allah's greatness so that we can maintain the correct perspective as we navigate through life. Allah is Greater. He is greater than material things. He is greater than the money we have in the bank. He is greater than our poverty and our problems. He is greater than our silly little egos and our exaggerated sense of self-importance.
Allah is greater than our family, or our racial identity. He is greater than our schemes and the squabbles we get into.
Allah is Greater, and that which is greater should never be put behind that which is lesser. So with this affirmation we remind ourselves of that which is most important in our lives. With this reminder we have the chance to keep things in the proper order in our minds and in our hearts.
Allah has no need of our praises. WE are the ones in need of the giving of praise to Allah. It's aids us in our spiritual edification by keeping us humble and trusting in Allah.It aids us in our Islam by keeping us focussed on the real work we were put on earth to do.
So the saying is neither childish nor nonsensical. It serves an important purpose.
I hope this answer helped you understand Islam a little better.
Peace be unto you.