Where digital clearly wins
A digital card is never out of date. Change your role, number or company once and every card you have ever shared reflects it — including the one you handed over eighteen months ago.
It also costs nothing per share, works when you have run out of physical cards, and can tell you that someone actually opened it.
Where paper still holds
In some rooms and some cultures, producing a phone rather than a card reads as careless. In parts of Asia the exchange of a physical card carries real formality that a QR code does not replicate.
Paper also does not need signal, battery or a working camera on the other person's phone — a genuine advantage in a crowded venue.
The honest answer is both
Carry a small number of printed cards for the occasions that call for them, and lead with digital everywhere else.
What matters more than either is capturing the other person's details. The card you hand over is worth far less than the contact you take away.