The paper stamp card is a good product. It costs a few cents, it never breaks down, it needs no network, and nobody has to be taught how to use it. If all you want is to count visits and give something away on the tenth, it does the job, and the subscription you would pay on top of it buys you nothing.
That is not where the difference lies. It fits in one sentence: a paper card cannot tell you who stopped coming.
What paper cannot know
When a customer puts the card in a drawer and never comes back, nothing happens. No event, no trace, no date. You never find out, because the only moment the card exists for you is the moment it is in front of you, which is exactly the moment the customer is there too.
A paper loyalty programme is therefore blind by construction to the one thing a business has an interest in knowing. It records the visits that happen and ignores the visits that do not, and it is the absence that costs money.
The other consequence is less obvious and more awkward: paper does not tell you who your best customers are either. You know them by sight, which works up to a few dozen people and collapses after that, and does not work at all if your staff changes from one shift to the next. The person who has come three times a week for eight months and the person who has come twice this month are holding exactly the same card.
What paper does better, honestly
There are cases where the card wins, and they are not rare.
Trust depends on nobody. A paper card asks for no phone number, assumes no smartphone, waits on no server that has to answer, and puts no question to anyone. For customers who would rather not hand over their contact details, that is a genuine advantage and not an objection to be overcome.
There is nothing to install on your side. No account, no tablet on the counter, no staff to train. The total cost of paper is the price of printing it.
It does not care about outages. Network down, phone flat, an update gone wrong: the stamp still goes on.
If most of your customers are passing through once, paper wins as well, but for a different reason: in that case neither option is worth much, and the cheaper of the two is the right one.
What digital actually buys
A digital card does everything the paper one does, with two properties the paper one cannot have.
The first is that it leaves a timestamped trace of every visit, attached to a person. That is what makes "who stopped coming" a question you can compute: with no dated history per customer there is no rhythm, and with no rhythm there is no departure from it. The detail of the calculation comes down to two thresholds and a few floors.
The second is that a channel back exists. Card stock is mute; a digital card lets you say something to somebody who is not standing in front of you. It is the only way to turn a detected absence into a visit, and it is also the part to handle with care, because it is the part that can irritate.
A third difference is worth adding, a more mundane one: the counter cannot be faked. A paper card gets stamped twice when the queue is long, and it gets photocopied.
What the two really cost
Paper costs the printing, plus the time at the counter, plus the lost cards (starting again from zero is the moment a customer gives up on the programme). Digital costs a monthly subscription, a few dozen currency units a month depending on the size of your list, plus the four minutes of setting it up.
At those amounts, the decision is not about price. One recovered customer a month pays for the subscription in most businesses, and one customer lost without your knowing costs a lot more than that over a year. The real cost of paper is not the paper, it is the information that never existed.
The question that settles it
It is not "is digital better". It is: do you have customers who come back and who you would like to keep?
If you do, the value is in what you learn, not in what the counter is printed on, and card stock cannot teach it to you. If you do not, keep the paper: it does very well what it is asked to do.
And if you do move from paper to digital, the thing that matters most is not resetting your regulars to zero. A customer who had seven stamps has to start with seven stamps, otherwise the new system costs them seven visits and they will not forgive it. The comparisons between tools take up that point, along with the cases where Kanz is not the right choice.