IMO it will depend on what the higher price is for. Are you paying a higher price for one amp over another because there are higher quality components used? Are you paying a higher price for a proprietary design or circuit board? Are you paying a higher price for a better built product that brings tech support and help.
Or are you paying a higher price for an amp that is not built well with low cost components, off the shelf circuit boards. Are you paying more to cover marketing and advertising costs that add nothing to the sound. Are you paying more for an amp from a company that has to pay retail rent, heat, electric, and employees to sell them. Are you paying more for an amp that is sold by an independent dealer with a 200% mark up yo cover his business cost.
I would end with the answer to your question as being yes a more expensive amp can sound way better based on price if you are putting your money into areas that add to the sound not the fring costs that add nothing to the sound only to the cost.