Old axes tend to be better because they were produced when the axe was used as a everyday working tool. You can find very good deals in very good quality old axes, but you have to be very aware of the axe you are purchasing. Standard axe owners axe mantaining knowlegde is low, you have to take in account this is a reality for many years for now. So you have to be aware you don't purchase any piece which has had a bad manteinance history like this,
The bit of that axe is as soft as iron, a friend of mine has had to heat treat it again. It's very usual to find refitted vintage axes nowadays, I don't like it. You can clean all the marks of the axe I have shown and you won't know your purchasing mistake till you try it in the wood.
If you want to find that type of quality in actually produced axes, the best you can do is to stick to old school axemakers. Council Tool is a good option, same as Jauregi or Mueller. I have seen the heat treatment in those companies, CT and Mueller in videos, and they use old school techniques. You won't find bad steels in the companies we are speaking about, proper heat treatment is more important than steel in an axe.
About steels, at same hardness higher carbon steel is not better. Between the most important qualities of an axe is its toughness, an axe at more or less at 55HRC and with more or less 0.5% of carbon is at the best point it can be for a general use. The same can be said about alloys, the less alloying elements you can give to a steel mantaining the desired quality, the best axe you are making. A clear example of this are the racing axes (I'm speaking about my experience, those used at Basque competitions and trainings), people tend to think their steel is a superalloy, this is not true. They tend to be medium tool steels with very well studied heat treatments, as an example their carbon variates but tends to be 0.6-0.65%.
If you are thinking to buy a Council Tool Velvicut I advise you to buy a FSS instead. I own both and I have not found any wear resistance difference between them. If we assume both of them have the same hardness, I think 4140's higher amount of carbides help to it's lower carbon percentage when we compare it to the 5160. If we look to toughness the 4140 is toughter.
At the price you have mentioned I would buy the standard Council Tool.