Cook's tentativeness can be misleading.
Like last time, McCullum middled questions from the packed amphitheatre as if this captaincy lark is a doddle. He commands respect with his side in the ascendancy as the world's third-ranked test team. McCullum spoke with candour about their self-belief in an era when they will enter the home of cricket with one of the strongest New Zealand XIs.
In contrast, Cook shuffled about the microphone-laden front table like he was in the Mastermind chair. His specialist topic, which he said was "irrelevant", was 'Could he play with Kevin Pietersen again?' Whatever tangent the media conference took, it gravitated back to the controversy over whether the in-form former England batsman should be back in the test side. The scrutiny was relentless, but necessary, as local media seek answers to what seems complicated back room politicking.
They eventually got the concession they were after: "I do agree with the decision, yes," Cook said. "But the decision was made by those two [chief executive Tom Harrison and director of cricket Andrew Strauss]. That's what their new roles are, and they made that clear when they were talking to the team.
"This thing has gone on for 15 months now, and we've got to start looking forward as a side. For me, that is leading the players out tomorrow at Lord's trying to win a test series."
In contrast McCullum was at liberty to explain his views to a receptive audience.
His biggest problem was that it was "cold" after spending the last few weeks in the heat of the Indian Premier League.
He sympathised with Cook and England's position, having been on the periphery of the Ross Taylor captaincy saga in late 2012.
"They're going through some challenges; we've been there as well. I understand teams can go through that but they're still stacked with world-class players and will be a tough proposition in these conditions.
"[In the New Zealand team] everyone needs to totally buy-in but every environment is different. Without being part of the England team's inner sanctum it's difficult to make an informed decision about KP and the relationships in the group. It would be foolish to make outlandish statements. I'll leave those questions for when Alastair gets here."
The pitch appeared green from a distance but McCullum wasn't certain winning the toss meant fielding because it "looked a bit dry" under the layer of grass, some of which will be shaved.
"It also depends on the overhead conditions. If there's cloud around, we'll look to bowl."
McCullum was asked whether this was the strongest side New Zealand had taken into a Lord's test.
"I don't want to be disrespectful to those who have gone before. This is the best team I've been part of but we're not the finished product. We've made significant changes but we're only No.3 in the world.
"I want the guys to play with a free spirit, to earn the right to be instinctive and aggressive and, if we're faced with the same situation [as 2013] I'd hope we would fare better. The guys are more mature and have put in better performances over the past couple of years."
McCullum said coming from the IPL shouldn't cause an issue. He cited last year in the West Indies as an example when they scored 508, eventually winning the test by 186 runs. In 2008 McCullum arrived at Lord's from the IPL and scored 97 from as many balls.
