Guess I'll add some thoughts since you haven't gotten any response yet, but take this with a grain of salt. I'm assuming we're discussing these materials in the context of use for a hatchet/axe.
4140 is a lower carbon steel commonly used in hammers. It does not have enough carbon to get very hard, but is known for great impact resistance. This means you would probably have a hard time actually breaking an axe head made from it, but due to its softness and corresponding lower strength, will probably get a fair amount of edge rolling and denting/impaction.
1060 is a simple carbon steel below the eutectoid point. Meaning it will form lath martensite, which is a tougher form than the plate martensite formed by higher carbon steels, such as 1095. At the relatively low hardnesses you mentioned, I would expect performance somewhat similar to the 4140 listed above. You'd probably never break it, but the edge would be more easily damaged if you whack a hard substance with it.
I am not familiar with N690Co. I have not seen spec sheets on it that give impact values. However, some googling shows that it's a stainless steel commonly used in folders. I would not expect it to be suitable for an axe at all. There is no stainless made that can approach the impact toughness of carbon steels, and if it's used in folders, that's another hint towards its best suited purposes.
Any of these steels would probably perform well enough for occasional general use- probably on par with your average hardware store hatchet. If that's all you need, you'll probably be happy. However, none of them can come even close to what's possible with good steels designed for such use, if you're looking for the "ultimate" blade. L6 for example should be just as tough while being harder, meaning it won't break or have a weak edge that would roll. And the shock steels like S7 or S5 should be able to blow them out of the water in terms of crazy impact resistance at high hardness. On paper, S5 is supposed to be tougher at 61 Rc than even L6 is when tempered down to 53 Rc. !!!!
