Check out the thread I posted earlier - people with far more experience in that thread can talk about the nuances.
AMEX doesn't publish their FX rates but they tend to be closer to Visa than MC.
Visa doesn't apply the rate until the charge actually posts. MC charges the rate on the day of purchase. It's therefore believed that Visa charges ~1% to cover the spread between when you purchase and when the charge posts and they actually apply the FX.
The result is Visa can actually end up lower if there's a big drop between when you purchase and when it posts (e.g., if you bought something the night before Brexit, Visa you'd benefit from the pound drop the next day, MC you would not).
It's also seems that some CC issuers are willing to eat this 1% (e.g., my Schwab Debit Visa tends to be have a better rate than my CSP - most likely Schwab is willing to cover that small spread that Visa charges or has negotiated with Visa to remove it) whereas Chase has chosen to pass it on.
As noted upthread this is why I almost exclusively use on of my MC when traveling (typically Prestige or Premier) unless there is a specific reason to use my Visa (e.g., Hyatt Visa at Hyatt hotel, CSP for insurance, etc.)
EDIT: Just to add, it's believed that Visa uses the highest rate on a given day whereas MC uses either the average or the close.
On the day in question (June 26th) it looks like the highest rate was 1 GBP = 1.4371 USD so their rate is actually right in line with that. FWIW, the close was: 1 GBP = 1.3694 USD and the average was: 1 GBP = 1.4059 USD so MC appears to be just below the midpoint
It's a pain and it means you may have to put the Visa in the wallet for international travel, but with those numbers I unfortunately don't think you are going to get anywhere with CFPB since their rate came in just below the high of the day.
Source:
https://www.poundsterlinglive.com/be...-on-2016-06-26