What are the advantages of holding an EU money transmitter license versus operating under a bank’s umbrella?

A couple of things here… at the time of writing this answer (see snapshot below).

1. There is no money transmitter license in the EU. The word money transmission and money transmitter license is the US terminology for a money transfer/e-money license.
2. The EU does not have a surety bonding requirement like the US.
3. Bank-led sponsorship (which you are calling umbrella coverage), is a perfectly okay method of going forward with your plans. It just ties everything to that bank.
4. Tomorrow when you might want to shift to a bank or a non-bank institution that offers a better product or service, you won’t be able to go, because you’re stuck with the existing bank.
5. Even if you get your own licenses, you will have to negotiate with the bank, pre-hand that the clients will be transferred to you (EU allows passporting of KYC information), as and when you get your own license.