In this paper, we compare four branch and bound algorithms for solving the extended trust region subproblem (eTRS). In recent literatures, Buchheim et al. used the SDP relaxation for solving nonconvex quadratic program, their branch and bound algorithm focused on branching along axles, this algorithm is valid for eTRS. Later, Burer et al. studied a SOC-SDP relaxation for eTRS. Combining Buchheim et al.'s branch and bound framework and the SOC-SDP relaxation leads to a new algorithm for eTRS. Furthermore, Lu et al. proposed a new convex relaxation for nonconvex quadratic program over convex quadratic constraints, that is made of SDP relaxation and some additional linear constraints, their branch and bound algorithm focused on branching along eigenvectors associated with negative eigenvalues of the matrix of the objective function, such algorithm is also valid for eTRS. Similar with Burer et al., Second order cone constraints can be added to Lu et al.'s relaxation and the same branch and bound framework is adopted. Computational results show that the last algorithm is the most effective.