Both sides have been in the headlines for the wrong reasons since the Windies' series-tying win in Port of Spain.
The home side's captain Denesh Ramdin slammed his side's attitude, after they still had to chase down 93 runs for victory despite an innings victory on the cards when they needed only another two NZ wickets.
The Windies had a 27-run lead late on day four, before tail-ender Mark Craig combined with BJ Watling for a 99-run partnership to postpone the hosts' win.
Ramdin labelled the Windies' attitude as "lazy", despite their 10-wicket victory seeing them break a run of six Tests without success.
Meanwhile, the Black Caps have some concerns with part-time off-spinner Kane Williamson reported for a suspect bowling action.
Williamson has bowled 16 overs this series, for the tidy overall figures of 2-44, but the ICC have requested the batsman undergo tests on his action.
The 23-year-old is available to bowl in the third Test at Kensington Oval.
The West Indies snapped a five-Test winless run at the venue when they last appeared in Barbados, downing Zimbabwe by nine wickets in March 2013.
The previous meeting between the two nations here was in 2002, with the tourists running out 204-run winners.
The only survivors from that series are West Indies batsmen Chris Gayle - who was playing his 22nd Test - and Shivnarine Chanderpaul, who was in his 57th Test.
And their seniority has shown so far this series, with the pair the equal-highest run scorers for the hosts with 155.
Also in form for Ottis Gibson's side is Kraigg Brathwaite, who came in for the second Test and excelled with a first-innings 129.
New Zealand have the series' three highest scorers - Tom Latham (274), Williamson (209) and Watling (177).
Windies paceman Jerome Taylor (10) leads the wicket-taking this series, ahead of team-mate and towering off-spinner Sulieman Benn (nine) and Black Caps leg-spinner Ish Sodhi and off-spinner Craig (both eight).