Actually my experience is completely different from yours
Perhaps you asked for refund in GBP while you paid in Euo
I alway pay in euro and ask for refund in euro
Then the actual amount back to my USD CC is determined by daily wholesale rates of Visa when the transaction is processed. That's the best rate one can get
My girlfriend always wants cash instead of CC refund so she always gets hit by lower % back due to higher processed fees global blues or premier tax slashes on the transaction
If you ask for CC refund you get the full € listed on the forms back while cash you don't!
Actually, it is stated on Premier Tax envelopes that they take about 3-4% (They stated a range which I am not sure if I recall correctly now) from a rate (think central bank or some other bank). It is not base on the daily wholesales rates of Visa for sure.
I was thinking I may get the Visa's rates and be slapped with a 2.5% admin fee since the refund is in the EUR which is a different currency from my card. In the end, the refund was made in my currency with no cross border admin fee slapped on me. The refund could be processed by the Premier Tax in my country since I will incur a cross border admin fee for a transaction in my home currency that is carried out overseas. The exchange rate was worse than if the refund was made in EUR and my bank takes a 2.5% admin fee from me.
While most merchants in France practice a deduction of 10% of the overall VAT refundable as additional admin surcharge and the cash refund managing agent charges a EUR 3 or EUR 3.50 surcharge per receipt, this is not always the case in other Europe countries. If I recall from Global Blue refund form, France and UK are the 2 countries where the cash refund agents will charge a fee.
Given the case, it may be wiser to opt for cash refund if the purchase and refund is not done in France. Otherwise, my reason to opt for cash refund at the airport is the sense of security that the refund is definitely completed before one leaves the country and not withstand the agony of waiting for refund.
However, my personal advice is that if the intend is to pay via cash and refund is to be done in cash, do at least pay part of the bill by cc. In case the cash refund agent refuses to honor the refund, you can still fall back on cc refund as a last resort. I was refused cash refund at CDG airport just earlier this year.