an axe wins hands down for me.
saws blunt and most cannot be sharpened and the ones that you can sharpen can only realisticly be done in a workshop. you can't shape or split wood. saws tend to be fairly fragile compaired to other tools.
knives are good and yes you could fell trees but only very small ones and it would blunt or easily damage the blade by pushing it to tackle larger jobs.
with an axe you can efficiently fell, sned, section and split a tree into firewood. like a knife it can be easily maintained in the field with basic tools. building shelters is a breeze with an axe. its only downfall is fine carving but you could gut fish or skin game at a pinch.
of course all three would be much better or a billhook as Zingmo would be a good option for an 'only one tool' situation (if one exists?).
i think i would choose an axe, 2- 2.5 pounds and a 28 inch handle is hard to beat but nobody uses them? i can understand issues with carrying one backpacking in the uk but for fixed camps it blows others out of the water imo.
pete