I always used to underrate Button too but looking back I have no idea why. Look at 2006, his first season alongside Barrichello. Barrichello was fresh off facing Micheal Schumacher in 2005, where he scored 61% of Schumacher's points on a points per race basis (points divided by races without mechanical DNF). Then in 2006 Barrichello faced Button where, on a points per race basis, he scored... 50% of Button's points. Button carried this advantage over Barrichello through into 2007 too, and lets not forget 2005 where he dominated Takuma Sato 37-1 in points. But nobody seemed to notice.
Obviously Button wasn't performing at a near-Schumacher level all of the time, he was outscored by Barrichello in 2008 and didn't beat him all that convincingly in 2009, to name just a couple of obvious examples. But even so.
Going back to Alonso vs. Button, Alonso leads the overall battle 15-9 in qualifying, 8-7 in races and 35-33 in points, although Alonso has suffered more mechanical DNFs and missed 2 races outright.