I have watched people get this wrong in both directions, and the second direction is more common.
The first mistake is refusing the new thing entirely, which mostly costs you convenience. The second mistake is using the new thing everywhere because you paid for it, and that one can cost you the room.
Where paper still wins
A formal first meeting with a senior counterpart. 名刺交換 is a ceremony with a shape. Both hands, the card turned to face them, a small bow, a moment of actually reading what you were handed rather than pocketing it. That sequence carries meaning, and it is not yours to redesign on someone else's time. Lead with paper. You can tap later, once you have earned the right to be slightly informal.
Any room where you are the junior person. Not because tapping is rude, but because introducing a novelty makes the moment about you and your card. When you are the most junior person present, the moment should not be about you.
Groups. A tap is a one to one gesture. Around a table of eight it becomes eight separate small transactions while seven people wait, and the thing that was supposed to be efficient is now the slowest part of the meeting. Paper goes around a table. Let it.
Anywhere the other person looks uneasy about it. This is the one that requires actually paying attention. If someone hesitates, or holds their phone slightly back, or says "ah, I am not sure about mine", you have your answer. Do not persuade them. Switch.
Where tap wins clearly
Standing up with a drink in one hand. On a factory floor. At the end of a conference day when you have run out of paper and the person in front of you is the one you actually wanted to meet. In any conversation with someone whose title or number is about to change. With anyone under about thirty five, who will usually reach for their phone before you have finished the sentence.
And in the situation nobody plans for: you left the card case in the other jacket. The profile is a web address. You can still exchange details.
The rule that covers all of it
Never make the other person do technical support.
If it does not read on the first attempt, do not explain NFC, do not ask them to open settings, do not try a second and third time while the silence grows. Say the address out loud, or show the QR, and carry on with what you were talking about. Two seconds, no commentary.
The card is supposed to make you look prepared. Everything above is just protecting that.
Carrying both is the answer
People frame this as a decision, as though you have to pick a side. You do not. A card case with paper in it and a tap card in your wallet is not a hedge, it is equipment.
The point was never to stop using paper. It was to stop the specific failure where the paper is out of date, or gone, or in a drawer somewhere being counted as a lead.