From the exception.log I have this, which I cannot figure out what means, exactly.
Exception message: SQLSTATE[23000]: Integrity constraint violation: 1452 Cannot add or update a child row: a foreign key constraint fails (`shop`.`eav_attribute_group`, CONSTRAINT `FK_EAV_ATTR_GROUP_ATTR_SET_ID_EAV_ATTR_SET_ATTR_SET_ID` FOREIGN KEY (`attribute_set_id`) REFERENCES `eav_attribute_set` (`attribute_set_id`) ON DELETE)
Changing eav_attribute_set from MyISAM to InnoDB fixed this!