I wouldn't recommend a local walmart (made in China junk) socket wrench set for a serious mechanic. If you use an axe once in a while, and don't really know what you're doing, the 15 euro one will be fine.
But, I've split a lot of wood with an axe, and used my small forest axe to clear downed trees. There is a difference between the cheap tool and the quality tool. Everyone who has ever tried one of my axes says the same thing, "Wow! That axe is awesome! It works so much better than other axes I've used." That's quickly followed by "Hey, can I borrow your axe?" for the rest of the trip...