"In a race? (Alonso is) a bigger challenge, a more consistent challenge. He's always there," Button, the 2009 world champion, told reporters at the Abu Dhabi Formula One Grand Prix on Thursday.
"On some race days, Lewis was untouchable, on other race days it was like 'where is he?'. Lewis is a different driver now, more experienced, but Fernando's always there, he's always competitive.
"If he's in front of you, you're holding on. And if he's behind you, he's pushing you along," said Button, who was replaced by Alonso at Renault in 2003.
Button and Hamilton, now a triple world champion, were team mates at McLaren for three years from 2010 until Hamilton switched to Mercedes.
Button remains the only team mate to have beaten Hamilton over a season, finishing second in 2011 when the younger Briton ended up fifth.
Hamilton is also the only one of Alonso's team mates to have beaten the Spaniard over the space of a year, ending his 2007 debut season ahead of the double champion on results after finishing level on points.
That record looks set to end this year, with Button currently five points clear of Alonso in their first year together at McLaren with only the final race at Yas Marina to come on Sunday.
"Working alongside Fernando has been great, and we do learn from each other a lot because we have both had such a long career in Formula One," said Button.
"We come together with all that experience and it really helps us with the limited running we have had this year. It has helped this team in terms of a direction for next year.
"Giving great feedback from two experienced drivers, that is what is going to move this team forward the most."
McLaren have endured their worst season in Formula One after their new partnership with Honda was hit by endless engine problems.
Button, the most experienced driver on the current starting grid, and Alonso have suffered multiple penalties and had to start from the back of the grid. The team look set to end the campaign ninth of 10 teams.
Hamilton's dominant Mercedes team have meanwhile won 15 of 18 races with 11 one-two finishes. Hamilton, who clinched his third title with three races to spare, is chasing his 11th victory of the season in Abu Dhabi.
(Reporting by Alan Baldwin, editing by Ken Ferris)
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