XE.com is also our comparator. You need to look at the day the transaction hit.
Within the day the rates can change but we have only seen variances in the third and fourth decimal point. My understanding is that there are several 'settlement' times during the day. Not a banker so I do not really know.
When we switched,we knew our Visa card added a 2.5 percent fee on foreign transactions. We also found that our card was out by about 3-3.5 from the XE.com rate (2.5 or admin plus another point because they are greedy).
Same for ATM, but worse. Our bank was adding 2.5 percent to the XE.com rate. Our bank was charging $5 for the ATM transaction and giving us a terrible exchange rate. In some cases we were also paying at the foreign ATM end as well. It adds up so we smartened up and flew right.