Two different routes for the same invoice
A card payment through Stripe passes three layers on a cross-border invoice: the card fee, the surcharge for a foreign card and the conversion. On the $5,000.00 example that is $75.25, $82.50 and $96.85.
With Wise, the client pays your US account details by ACH as if you were a local supplier. There is no card and no border, so the first two layers do not exist. What is left is the conversion, which Wise does at the mid-market rate with a published fee of 0.29% from dollars to euros. Hence $14.50.
The gap grows with the invoice, because both costs are percentages: on $20,000.00 it is $959.65. Below a few hundred dollars it hardly matters, and the convenience of a card link can be worth more than the saving.
In practice many freelancers keep both: Wise details printed on the invoice for business clients, and a Stripe link for the client who will only pay by card.