I haven't been comparing them to their most similar competitors. Since they're a payments-processor first and foremost, they compete in Europe with Barclays, UniCredit, BNP Paribas, PaySafe, Lloyd's, PayPal Global Payments, BofA, Stripe, Square, JP Morgan, iZettle, WorldPay, Fiserv, Societé General, Credit Agricole, & Credit Mutuel, among a very fractured European payments market.
Biggest problem being Stripe, since it's private, there's no way to value it, it's unprofitable (no disclosures required) and they're global.
Adyen is also, funnily enough, one of the least known payments processors, regarding the UK, France, Germany, Italy, & US.
Adyen is not far behind PayPal and Square in terms of net perception of processors by the merchants in those 5 countries. The avg is 66% for all 30+ companies being asked about. Adyen hit 69%, PayPal was 76% and Square was 73%.
Merchant acquiring-wise, WorldPay (Fiserv subsidiary) was #1 in Europe last year with 11% ($404B in transaction value), Adyen is 11th at 3% ($116B).
But in terms of strictly online merchant acquisition, Adyen is 4th behind Barclays $172B (18%), WorldPay $156B (16%), JP Morgan $111B (12%), with $102B (11%).
This is a goliath $80B company, happy investing!