That's a bold claim - can you quantify the savings available from buying from an FX broker, versus a bank ?
And, for EUR 2000, would those savings justify the overhead of going somewhere other than your own branch ?
From my own experience i would say 90% of the time an fx broker will offer a better rate of exchange than you would get from a bank on transactions over €20k.
There is a lot of literature out that would agree with me, there is alot of brokers out there and you can play them off against each other like car insurance companies.
Give it a try with a mock transaction, get a rate from your bank and call a few fx brokers such as travelx, travelmate, omnisfx and i will be astonished if the bank will offer the most competitive rate.
on anything under 10K the bank is likely to comparable on the rate and the savings will prob be too small to warrent using a broker.
the majority of banks have a flat rate of exchange - non dependent on the size of the transaction, compared to fx brokers who have lower overheads and are more aggressive.
also check out this competitive table, which highlights the difference methods of currency exchange
just to let you know i work for a currency broker and have a currency advice website, but this fact doesn't mean i am wrong on this point