The price differences in HCOL and LCOL cities stem mainly from the forces of demand and supply in the market. Of course, this is accentuated by the population in an area.
Before leaping into a new city, whether an HCOL or LCOL area, you should brainstorm several factors that may ultimately dictate your overall quality of life in your newly found home, for clarity of your moving goals, you can narrow down your considerations into personal factors and financial factors.