We are the only one thinking there's a competition between both assets. The two are different and unique in their own ways. While one already has the trust of the people for been a safe heaven, the other is been seen as a very volatile (which it's), speculative assets that has no real life usages. The only relationship I can think off is both been a better alternative to the fiat system, if you're looking for a way to escape the Ponzi scheme called the fiat system, you can used that worthless fiats to buy gold (if you intend taking less risk).

Or buy bitcoin (if you'll be comfortable with the risk it posses) and do understand that it has greater chances of outperforming any assets since it's relatively new and has a better technology and mode if operation which is decentralized and also digitized unlike gold that's the direct opposite.