Yes. MoonPay requires a minimum purchase of €20 and charges either 4.5% per transaction or a $4.99 minimum fee. This is not an additional fee but instead is taken from the purchase total. They currently support EUR, GBP or USD payments.
Additionally, once you've created an account with MoonPay, there is a monthly limit of 150€ per person. After a successful identity verification process, the daily limit is increased to 2,000€ and the monthly limit to 10,000€. The daily and monthly limits include the fees.
Dapper collects no fees when you purchase ETH through MoonPay.