Here we look at the figures relating to Tests between these teams, after England won 3-0 in 2022.
First, a summary of all Test results:

As NZ was a weak team for a long time, England leads by a large margin. There have been a few 3-0 sweeps in the past. NZ has done a little better at home. They have won a few series at home and away.
We now proceed to individual performances:
Most runs (750 and above):

JE Root now has the most runs (1388) in E v NZ Tests. Next is GA Gooch with 1148.
Among current NZ players, KS Williamson has the most runs (853) which is far behind JG Wright’s record of 1518.
The most centuries are 5 by MD Crowe, and the most fifty-plus scores are 11 by Wright and R Taylor.
Highest innings scores (150 and above):

The highest scores in this series were 190 by DJ Mitchell and 176 by JE Root, far behind the triple centuries of Hammond and J Edrich. Hammond’s 336* was a world Test record (surpassing Bradman’s 334) until Hutton overtook it with 364 in 1938.
Highest batting averages (Minimum 20 innings and 35.00):

Cowdrey leads by a large margin. Root (49.57) and Williamson (37.08) have the highest averages among current players.
Highest strike rate (Minimum 1000 balls faced and 45.00):

McCullum leads by a large margin. Next is Stokes with 63.32. The highest by a current NZ player is 49.43 by Mitchell.
Bowling-most wickets (30 and above):

Sir Richard Hadlee leads with 97, and current player Broad is next with 84. Boult (70) has the most by a current NZ player. He is in the fourth position after Anderson (74).
Hadlee has the most 5wi (8), and Underwood the most 10wm (3).
Best innings bowling (including all 7wi):

No major innings hauls in this series, although Anderson and Broad have done well in the past.
Best match bowling (including all 10wm and above):

There was one ten-for by MJ Leach in this series.
Best bowling average (Minimum 2000 balls bowled, all instances):

DL Underwood leads by a large margin. TA Boult has the best among current players, followed by Anderson, Broad and others.
Underwood has the best bowling average, economy rate and strike rate. The second-best are Willis, Illingworth and Caddick respectively.
To be continued.