I keep hearing people call Bitcoin “digital gold.”
But gold has been around for thousands of years, and Bitcoin is only ~16 years old.
You're correct to say gold has been existing long time before bitcoin. Infact gold has been existing in thousands of years now and has been in used for human values for over 600 years while bitcoin has only exited in 16 years now.
The bone of contention now is which of the assets that holds better value or to say which has obtained higher potential values. Right?
So now I'm thinking of dropping you a shot the market charts to do the justice. So can take some glance of their All Time High which should be a view of their historical highest price since they both ever existed to be in used for values.
This is for gold
This is for bitcoin 
You can judge this by their time frames and their market performances up to date.
So it's literally not about which has been the first to exist but about which has more liquidity to uphold potential values I'm the long term. Obviously bitcoin is doing it as it All Time High can't even be compared with Gold despites gold market cap being higher.
Do you think Bitcoin can really replace gold as a store of value — or should they just complement each other?
Bitcoin isn't there to replace gold or any other commodity. It's individual, institutions and the governments right to deicide which to store their values on. Currently gold and bitcoin are both good store of values which are good for diversifications of investment but bitcoin takes the lead due to it digitality and decentralizations given attractive edges for users.