As you have posed the question, I'd have to say that NickE has the best possible answer.
The first two digits of the steel grade (10) indicate a plain carbon steel (no alloying elements other than a small amount of Manganese). The last tow digits (45 or 55) list the aim carbon content (that is 0.45% and 0.55%). Carbon has a very strong effect on the hardness of the steel, in all conditions. So, with both steels in the same metallurigcal condition, the 1055 will be harder.
The optimum hardness for a steel is very dependent on its application. The optimum hardness for a steel nail would be very different than for a steel drill bit. You mention kinves, and to hold an edge, it is very important for the blade to be very hard, so I'd guess that in this application, they are really after maximum hardness.
The maximum hardness of a steel is nearly entirely dependent on carbon content. As carbon increases, so does maximum hardness. This relationship begins to level off at around 0.60, so, for for some knife applications, there may not be much advantage to exceeding 0.60% C, hence the choice of the 1055.
You also mention that 1045 being more cost effective. Why do you believe that? There are many factors that enter into cost, but the base carbon content is not generally one of them. You would have to examine the factors that are making the 1045 more cost effective to understand the trade-off between maximum hardness (edge-holding ability) and cost.
rp
