DS 1307 stays behind in time day by day...

One possible issue is that watch 32768Hz crystals are designed for the average temperature of a wristwatch (close to body heat for 2/3 of the time). You might find it keeps better time if kept at 30C rather than room temp.

Also crystals are cut for a specific load-capacitance - if the crystal is not designed for the oscillator it will run somewhat out of spec.