The best option to get more Baht for Euro or Dollar is to bring cash. It take a bit of searching in the street, to find the bank with best exchange rate, but it is worth it.
If you arrive at the Bangkok airport go completely down to the AirportLink and go to the exchange offices there. Never change money in the arrival hall!
Take the higher value notes with you as $/€ 100 - 500 notes get a higher exhange rate.
Last year we found a rate that was about 8% better for cash exchange of Euro, than the rate I got from my bank with all costs when taking money from the ATM with Maestro.