BTW.... cone six is considered "mid-range".
In terms of strength of the pottery, impact on glaze, or both?
It is just the standard term for that firing range.... cone 4 to 6.
Clay bodies don't happen to work out as a "linear progression" for strength qualities by the firing temperature.... although some folks will try to tell you that. Some cone 04 bodies are stronger than some cone 9 bodies, and every other combination you can think of. Ther are lots of measures of "strength" also...... impact resistance, tensile strength, compressive strength, lateral shear, and so on.
The higher one fires, the more silica (SiO2) there can be in a glaze formula. As a very general rule, the higher the silica content, the more durable the glass can be. Pure silica glass is very physically strong and chemically inert.......but it melts at such a high temperature that it is not useful for pottery. So we lower the melting point with fluxes. The higher the flux to silica ratio....the more compromise in the qualities of the glass produced. Some particular flux choices compromise the qualities more than others too. It is a complex science.
One firing range is not "better" than another, they are just all different.