demo, MySQL - rextester

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#MySQL 5.7.12
#please drop objects you've created at the end of the script 
#or check for their existance before creating
#'\\' is a delimiter

DROP TABLE IF EXISTS table_new;
CREATE TABLE table_new (name varchar(55), surname varchar(55), birthdate datetime, birthplace varchar(55));
INSERT INTO table_new (name, surname, birthdate, birthplace)
VALUES
    ('Jon', 'Skeet', '1975-03-31', 'Reading, UK'),
    ('Gordon', 'Linoff', '1973-11-20', 'New York, NY'),
    ('Balus', 'C', '1977-02-28', 'Warsaw, Poland');

DROP TABLE IF EXISTS table_old;
CREATE TABLE table_old (name varchar(55), surname varchar(55), birthdate datetime, birthplace varchar(55));
INSERT INTO table_old (name, surname, birthdate, birthplace)
VALUES
    ('Jon', 'Skeet', '1975-03-31', 'Reading, UK'),
    ('Gordon', 'Lindoff', '1975-11-20', 'Peekskill, NY'),
    ('Balus', 'D', '1977-02-28', 'Warsaw, Poland');

SELECT t1.*, 'table one' AS missing
FROM table_old t1
LEFT JOIN table_new t2
    ON t1.name = t2.name           AND
       t1.surname = t2.surname     AND
       t1.birthdate = t2.birthdate AND
       t1.birthplace = t2.birthplace
WHERE t2.name IS NULL
UNION ALL
SELECT t2.*, 'table two'
FROM table_old t1
RIGHT JOIN table_new t2
    ON t1.name = t2.name           AND
       t1.surname = t2.surname     AND
       t1.birthdate = t2.birthdate AND
       t1.birthplace = t2.birthplace
WHERE t1.name IS NULL;


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