Without climbing into the loft to get the rest of the details the position up to 1996 was :-
Out of 65 matches played (all league, except 1 Challenge Cup match) Town had won 38 and Haven had won 24 with 3 drawn.
Up to 1986 the score was 35 - 12 to Town but from 1986 to 1996 the score was 12 - 3 to Haven.
At Derwent Park Town have won 19 games to Haven's 13 and 1 drawn, but the score between 86 and 96 is 7 - 1 to Haven.
At the Recreation Ground Town have won 19 to Haven's 11 and 2 draws but again between 86 and 96 the score is 5 - 2 to Haven.
Up to 1996 there had been 17 seasons when the two teams didn't meet except Tow Towns Cup / Four Towns Cup etc.
Since 1996 I would think most matches have been in the Trains Cup (under various names) and if you want the details updated you will have to wait until I climb in the loft to check.