Copper does carry more current than aluminum and copper can carry more current with a smaller size wire than aluminum can with a larger size wire.
You can use smaller size copper wire to carry more current than you could with a larger size aluminum wire.
Aluminum wire is cheaper and lighter than copper wire and for overhead and underground service wire from the pole or transformer to your house the utility uses mostly aluminum wire.
That is because aluminum is cheaper than copper.
However some people will use copper wire from the weather head or meter box to the inside of the house.
Copper wire is also easier to work with and bend than aluminum wire and it lasts longer and doe snot oxidize like aluminum wire can.
Copper wire is always used inside the house because it's safer than aluminum and does not fall apart as easily and start fires.