Each link you posted points to two separate digital objects both for the "enjoyment of a piece", not the "ownership of the piece". Think of ownership of a piece as the certificate of authenticity.
The first link is on superrare. The superrare image can also be enjoyed by anyone. However, the (very small) link (https://etherscan.io/tx/0xd9e4971bef6d37807605e0eb635eb4b6d9...) to the transaction on the page, tells me the owner of the art piece is 0x053e84e80cfb38d672d53394de3dade1fbbacd25.
The second link is on your own homepage. You can claim ownership on the image (since it's on your homepage), which gives you the enjoyment of the piece. But you don't claim ownership of the art piece.
Now, who determines which one is the real one? Depends on the counter-party you're transacting with, and what they're willing to honor.
If I as the counter-party, am being sold ownership of the art piece from both you and 0x053e84e, I'd take it from 0x053e84e, for the same reason you tried to make: digital images are exact copies. He own the non-duplicable NFT and provably so, and can transfer that NFT to me.
If I as the counter-party is the creator of the piece, I can give certificate owners extra VIP features for the art piece, like a chance to meet me, or a one time delivery of a look-book of the making-of of the piece, I can do that, and be sure that it's not fake owners. The pleasure of ownership is different than the pleasure of enjoyment of the piece.
So what links the NFT (the certificate) to that particular image? Well, right now, it's conferred by Superrare. If this is turns out to be an issue, I can see ways around it.
One option is to use procedurally generated art, where the parameters are stored in the NFT. I think there may be others.