What's the difference between である and の in this sentence?

I believe 在る here is used not as part of the copula である but in the actual literal meaning of "to exist". This is partly hinted by the use of kanji instead of kana (though it is not a 100% indicator with manga).

I.e. the meaning is roughly:

"people tend to forget that they exist as humans"

and not

"people tend to forget that they're humans"

According to デジタル大辞泉, 在る can apply to people:

５ （その存在を客観的、抽象的なものとして捉え）人が存在する。居る。「昔々、おじいさんとおばあさんが―・りました」「異を唱える人も―・る」

６ この世に生きている。生存している。「世に―・る間」

5. (when perceiving existence as objective or abstract) people existing. to be (of an animate object). "Once upon a time, there were an old man and wife". "there are also people who disagree".

6. to live in this world. to exist "while [I] am/exist in the world".

Another example that comes to my mind is this line from the song Hemisphere (RahXephon Opening):

僕は灰になるまで僕で在り続けたい

I want to keep existing as me until I turn into ashes