$\mathrm{C}_4$ plants have better productivity because

Presence of photorespiration is considered as a wasteful and energy consuming process in crop plants which ultimately leads to reduction in final yield of crops. It is estimated that during $C_3$ photosynthesis, upto $50 \%$ of the $\mathrm{CO}_2$ fixed may have to pass through photorespiratory process, thereby resulting in considerable decrease in photosynthetic productivity. In $\mathrm{C}_3$ plants, there is little loss of photosynthetic activity on account of photorespiration which is absent in $C_4$ plants and hence they have better productivity.