For postgresql, existing Python 2 databases work fine with Python 3.

For mysql, they don't.  I've committed a patch to ensure both database
and connection encoding are set to UTF-8 with mysql with Python 3, to
allow non-ASCII characters to work properly in that case.  But existing
Python 2 databases use whatever the default MySQL encoding is, but store
UTF-8 bytes incorrectly labelled as being in that encoding (if for any
reason the default database encoding at the time of creation differs
from the default connection encoding, things would be worse that than).
 So I've documented in upgrading.txt that for mysql you need an
export/import to move to Python 3 (though it would be good to have a
more efficient way of changing the recorded encoding of the data in the
database without actually carrying out a character set conversion it, so
as not to need such an export/import).