Is it:
Giraffe
I am born high only to fall low, attention !
Giraffe babies fall out of their standing mothers.
Leopard and I share a similare taste for fashion.
Giraffes share a similar colouring to leopards.
I may be browsing for Charles's hypothesis on my evolution.
It's debatable but there is a theory that Giraffes evolved long necks to browse/eat high leaves.. Marius' answer mentions that neck-fighting was a factor.
My toes are even and It is as if I look upon them from heaven.
Giraffes have two toes on each foot, and look down on them from their heads high up on their long necks.
In this category, no one is larger then me.
Giraffes are the tallest land animal (largest is probably not quite right.. elephants are bigger). Largest even-toed ungulate? (hippo is probably larger) Largest Giraffidae? From OP: Largest ruminant.
If I keep fighting. Mine's will become bald, no more hairy.
From Wild Life Ranch Texas: "Giraffes’ horns, or ossicones, are cylinder-shaped, short, thick, and covered with hair. The male giraffe’s ossicones are generally larger than the female giraffe’s ossicones and are bald on top due to fighting with other males."
Me and my genus fight neck and neck for hierarchy.
Giraffes fight by slapping necks