It would be unwise to draw any conclusions from the contrast, however.
If the relaxed Englishman won a prize for the fastest loser in a McLaren-organised media challenge, although having Reuters as playing partner contributed in no small measure to the defeat, he is just as hungry as Hamilton to pocket a second Formula One title.
The 2009 world champion, who will take over from the 2008 winner at the Barcelona test on Thursday, made no excuses for defeat on the scuffed green baize and does not expect to need any when the season starts in Melbourne on March 18.
"Last year I felt that I did the best with the car I had, that I really grew with the team, really felt a big part of McLaren, not just a driver but a big part of the team," said Button, the 2011 overall runner-up after winning three races.
"The relationship I have with my engineers and mechanics is very good, and there's a really good understanding there," added the 32-year-old, who won his title with Brawn GP and then switched to McLaren for 2010 where he had to come to terms with being in what many saw as 'Hamilton's team'.
"There's nothing to fall back on and say 'This is the reason why we didn't win in 2012'.
"I'm very happy now with my position in the team, and winning the world championship with McLaren would be amazing," said Button, whose team started 2011 with an uncompetitive car but rapidly caught up.
"With any team it would be amazing, but with a team you've been with for two years and had such a good relationship with and feel a big part of after such a short period, it does mean more than just arriving and driving the best car."
Button had that in 2009, when Brawn emerged from the embers of Honda after the departing Japanese handed the team over to Ross Brawn and Mercedes made engines available.
The team's very first test was astonishing, with Brawn setting the pace right from the start. By the end of the second day, when Button was in the car, rivals knew the game was up.
The 2012 McLaren has not done that but stands out among the 'ugly' stepped-nosed new cars as the only one with an unbroken, elegant sweep. Red Bull's double world champion Sebastian Vettel said on Tuesday that its performance looked "very strong".
"There's nothing to say we're one and a half seconds quicker than anyone, there's also nothing to say we are not fast," agreed Button, who tested it first at the Jerez circuit last month and said the team was "on target".
"Our programme is our programme and we are just getting on with it. It feels nice to drive, I feel very comfortable in the car, and it does everything you expect it to. It's just developing it now for the first race."
The Briton enjoys a close and supportive entourage of his father, manager, physio and girlfriend at races, something Hamilton has sought to recreate this season with Mika Hakkinen's former manager Didier Coton joining him.
"I have the best manager in F1, the best PR man, best PA and best physio. So for me over the winter I've not refined anything in any way," said Button.
"It's good to be back. I feel very confident in my ability, and in my input into the car and the team feeling I'm doing my part. It's all moving in the right direction, so I'm happy."