The nematic susceptibility, χφ, of hole-doped Ba(1-x)K(x)Fe2As2 and electron-doped Ba(Fe(1-x)Co(x))2As2 iron-based superconductors is obtained from measurements of the elastic shear modulus using a three-point bending setup in a capacitance dilatometer. Nematic fluctuations, although weakened by doping, extend over the whole superconducting dome in both systems, suggesting their close tie to superconductivity. Evidence for quantum critical behavior of χφ is, surprisingly, only found for Ba(Fe(1-x)Co(x))2As2 and not for Ba(1-x)K(x)Fe2As2--the system with the higher maximal Tc value.