We report a doping dependent electronic Raman scattering measurements on iron-pnictide superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals. A strongly anisotropic gap is found at optimal doping for x=0.065 with $Delta_{max}sim 5Delta_{min}$. Upon entering the coexistence region between superconducting (SC) and spin-density-wave (SDW) orders, the effective pairing energy scale is strongly reduced. Our results are interpreted in terms of a competition between SC and SDW orders for electronic state at the Fermi level. Our findings advocate for a strong connection between the SC and SDW gaps anisotropies which are both linked to interband interactions.