I can only find their similiraties but in the eyes of most people, bitcoin and gold are in competition and would be trying to fight each other by increasing their values.
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 of operation which is decentralized and also digitalized unlike gold that's the direct opposite.
I can agree with the part of your statement. they have unique features. Of course yes! And Gold is a safe haven assets already. After the popularity of Bitcoin it also now acting as a safe haven. So the whale ( Not like retail traders like us) are moving huge volumes between these two assets. It cause to pumps and dumps. I can provide many examples that tally with my statement. A recent example is the last week Gold Chart and Bitcoin chart. please compare them carefully. So you will have a clear idea about my statement.