"Assess" is for the qualitative value and ' estimate ' is for the quantitive value . He assesses the quality and estimates the price. You can use here 'evaluate ' instead of 'assess' but not estimate . He estimated the cost or price of the toy . He assessed the material of which it is made .

To assess the quality means that you are looking at the good and the bad to determine if the toy is a good value and worth the price or if it would be a good toy for the child. After you assess a toy, for instance, you may determine that the child is too young for that toy. To estimate means simply that you try to determine an approximate price or value of something. Or you can estimate (try to determine) size, number, height, weight, time, etc.