Both
I am one of the riders that uses SPD type shoes and also non-cleated shoes. I like both styles and it mostly depends on how and where I am going to be pedaling. The only thing that should matter is what you are comfortable with and what you prefer. I have both recessed cleat type shoes and non-recessed type. I have two sided pedals, both side the same style, and two sided pedals with SPD on one side and non-cleated on the other. I also have one sided pedals that are SPD but no one sided platform. Lately I have been asking myself why so many pedals and shoes. I cannot answer that in a definitive way that makes sense. I have been using the platform shoe/pedal type more in the past year or so. I think it puts less stress on my knees, ankles and feet. I know for sure that my knees and feet get more sore, quicker when I am using the cleated shoe/pedal style. As for stiffness of the sole, I never really paid that much attention to it. I like comfortable.