Basics first. To have better bending strength, component should have higher section modulus means higher area moment of inertia. Yes. Axial strength does depend upon the cross section area. For same modulus, lower cross section component will have more axial deflection and stress than higher cross section component. The answer lesser self weight exhibits better strength in bending is not the correct way to answer the question. For same cross section, hollow pipe has higher moment of inertia than solid section due to which it has higher bending strength e.g  compare 10 mm diameter solid rod with OD 15 mm and ID 11.2 mm  hollow section rod. Both have approximately same cross section but area moment of inertia for the hollow section is higher hence higher bending strength. If both hollow and solid sections have same moment of inertia both will have same bending strength. Also note the question's answer also depend on the material used for both component.