Amidst conflicting views about whether soft cooperative energy detection scheme (SCEDS) outperforms hard cooperative energy detection scheme (HCEDS) greatly in cognitive radio, we establish the bridge that mathematically connects SCEDS and HCEDS by closed approximations. Through this bridge, it is demonstrate that, if the number of detectors of HCEDS is 1.6 times as that of SCEDS, they have nearly the same performance which is confirmed by numerical simulations, enabling a quantitative evaluation of the relation between them and a resolution of the conflicting views.