To understand why dips are harder than push-ups we need to know about the vital gym equipment and workout accessories. There adequate use and what exercise activates what muscle. Types of dips and push-ups. Which set of exercises is suitable for amateurs and target what muscles.
It is tough to differentiate between the two as dips and push-ups are different sets of exercise. Although both exercises target pectoralis major and minor, triceps and anterior deltoids muscles yet dips require a broader range of motion. Dips incorporate your whole body weight and extensive mobility. Also due to the angle used in dips, makes it much harder on your shoulders. Shoulder strength is required for both it is true but dips require more shoulders mobility making it more difficult.
Generally, beginners can do push-ups with the help of gym equipment and gym accessories they can introduce variations and hit specific muscles. Once they are done with push-ups the logical step-up set of exercises is dips. Which again can be done with variations using different workout accessories.
One can do a combination of both with alternatives.