Button matched Hamilton in races (in terms of wins they were close at 10:8 to Hamilton),
Button scored 3 more podiums than Hamilton in 2011 (Hamilton's "breakdown season") to give him a better overall podium comparison of 25:22.
But in qualifying Button never got anywhere near. It was 9 poles :1 pole in favour of Hamilton in qualifying. It was also 9:6 to Hamilton in fastest laps.
Button was a canny operator, beautifully smooth and quick on his day but he didn't have Hamilton's raw pace or ability to drive around a problem. Button's admitted as much in interviews over the years.
Rosberg was much closer to Hamilton than Button was.
But that's a side issue when comparing Hamilton and Vestappen. Hamilton had already beaten the reigning world champion and secured his own first world title by the time he got to Vestappen's current tenure in F1...Max needs to calm down in order to maximise his obvious ability. If he doesn't, he'll be one of those "what if" drivers that history is littered with.
Actually, thinking about it, I wonder if Max's meteoric rise to F1 is working against him. He was put in an F1 seat after only 1 year of single seater racing. Hamilton did 5 years in single seaters before his F1 debut (although lots of people moan that he got a winning car from the off, he showed his talent over the years to earn the opportunity). Alonso only did 2 seasons in single seaters before F1 but, having had a year at the back in Minardi he went and had a season as a test driver before getting back in a race seat. Vettel did 4 and a half seasons in single seaters (including test driver roles) before getting his own seat. Even Michael had 3-4 years of junior stuff before his break in to F1.
I think Max has basically been learning on the job and it's a difficult way to polish your skill set. I think he'd have been a real force in F1 if he'd had 2, 3 or even 4 years in junior formulae learning his trade, and more specifically learning about how other drivers behave. He's blindingly quick - we all know that - but it seems as if he's always driving relying on his reactions rather than experience when driving near other drivers.