Notable advantages of an axe over a saw is that the range of potential applications is much larger and the tool itself is far more resilient. Saws are much faster and less wasteful than axes in thick cuts, but are far more susceptible to damage that impairs their effectiveness and much more difficult to repair when that damage occurs. On top of that, they're essentially a one-task tool. Invaluable labor savers, but if you were trying to carry a robust tool that remained useful for extended periods of hard use and was kept in good shape with fairly simple and rapid maintenance, the axe pulls ahead quickly. There's a reason why logging camps kept a saw doctor in-camp and he was never short of work to do. They were given that honorific title on account of how involved and exacting the job was--we often describe axe maintenance as an art, but it pales next to proper saw maintenance. I have a profound respect for those who know their way around tuning up saws.