Horus was one of the big gods and (supposedly) so was Anubis. Really they are both (step) brothers so they must be on the same level of power. (In a cool way...Anubis is cooler then Horus or that's my opinion)
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Neither Anubis or Horus had reason to fight and find out.
In some cases, Anubis could be considered the brother of Horus as Isis was said to have raised Anubis - Anubis being the son of either Isis and Ra, of Osiris and Nephthysor of Set and Nephthys.
Anubis is better.I suppose he is also stronger,being half human,half a fearless predator.Even if Horus is called the God of War,and is said to fly like a falcon,Anubis is the God of the desert and the darkness.Recent studies also show that the egyptian jackal is some kind of grey wolf instead.So,Anubis would win.
By some accounts of Egyptian mythology the brother of Anubis was Horus.
Anubis is the son of Set and Nephthys. He is also the cousin of Horus. Anubis is the God of Mummies. Anubis is can appear as a jackal, a man with a head of a jackal, as a man or in his godly form. Hope this helps.