The first boat carrying about 55 mainly Syrian and Afghan migrants sank off the Turkish town of Ayvacik.
The second was carrying about 20 people when it sank off Bodrum.
Turkey has become a major transit point for people fleeing conflicts in Syria, Iraq and Afghanistan, and hoping to reach northern Europe.
Hundreds of thousands of migrants and refugees have entered the European Union since August, heading up through the Western Balkans.
The latest attempts to make the risky crossing from Turkey to Greece encountered strong winds and poor weather.
The boat that sank off Ayvacik was heading for the Greek island of Lesbos.
The bodies of four Afghan children have been recovered so far by Turkey's coastguard, the Anatolia news agency said.
Two more children - sisters aged four and one, whose nationality was not immediately known - died when the second boat capsized as it headed towards the island of Kos.
Turkey is hosting more than two million refugees from the conflict in Syria.
The EU is expected to finalise a plan with Turkey on Saturday that could see Turkey given both financial aid and visa-free travel for its nationals in return for more action on refugees.
Balkan countries, including Macedonia and Croatia, last week imposed new border restrictions, only allowing passage to people fleeing countries affected by war.
Hundreds of migrants from Iran, Morocco, Pakistan and other nations clashed with police on Thursday while trying to force their way over the Greek border into Macedonia.
Macedonian riot police were seen hitting protesters with batons.
On Friday, Mark Rutte, the prime minister of the Netherlands, which takes over the EU's rotating presidency on 1 January, warned the EU risked collapsing "like the Roman Empire" if its borders were not properly protected.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
Six children have drowned as two migrant boats carrying them from Turkey to Greece sank in the Aegean Sea, Turkish media say.