Both months are a nice time to tour Turkey. The largest summer crowds are gone. The hottest temperatures are gone. Normally blue skies and pleasant temperatures remain :)
Rain chance does increase in October--particularly in the Black Sea region and İstanbul. Except ideal hiking weather in Cappadocia.
I went mid Oct and it was absolutely perfect climate for us. Sunny and warm all day, then starting to cool couple of hours before sunset.
We're from UK so a bit of sun is like summer. You might find it colder coming from the heat & humidity of Bangladesh
I would choose October over September.