This work deals with the $H^1 $ condition numbers and the distribution of the $\tilde \beta _{N,M} $-singular values of the preconditioned operators $\{ \tilde \beta _{N,M}^{ - 1} W_{N,M} \hat A_{N,M} \} $. $\hat A_{N,M} $ is the matrix representation of the Legendre spectral collocation discretization of the elliptic operator A defined by $Au: = - \Delta u + a_1 u_x + a_2 u_y + a_0 u$ in $\Omega $ (the unit square) with boundary conditions $u = 0$ on $\Gamma _0 $, $\frac{{\partial u}}{{\partial \nu _A }} = \alpha u$ on $\Gamma _1 $. $\tilde \beta _{N,M} $ is the stiffness matrix associated with the finite element discretization of the positive definite elliptic operator B defined by $Bv: = - \Delta v + b_0 v$ in $\Omega $ with boundary conditions $v = 0$ on $\Gamma _0 $, $\frac{{\partial v}}{{\partial \nu _B }} = \beta v$ on $\Gamma _1 $. The finite element space is either the space of continuous functions which are bilinear on the rectangles determined by the Legendre–Gauss–Lobatto (LGL) points or the space of continuous functions which are linear on a triangulation of $\Omega $ determined by the LGL points. $W_{N,M} $ is the matrix of quadrature weights. When $A = B$ we obtain results on the eigenvalues of $\tilde \beta _{N,M}^{ - 1} W_{N,M} \hat B_{N,M} $. In the general case we show that there is an integer $N_0 $ and constants $\alpha $, $\beta $ with $0 < \alpha < \beta $, such that if $\min (N,M) \geq N_0 $, then all the $\tilde \beta _{N,M} $-singular values of $\tilde \beta _{N,M}^{ - 1} W_{N,M} \hat A_{N,M} $ lie in the interval $[\alpha ,\beta ]$. Moreover, there is a smaller interval, $[\alpha _0 ,\beta _0 ]$, independent of the operator A, such that if $\min (N,M) \geq N_0 $, then all but a fixed finite number of the $\tilde \beta _{N,M} $-singular value lie in $[\alpha _0 ,\beta _0 ]$. These results are related to results of Manteuffel and Parter [SIAM J. Numer. Anal., 27 (1990), pp. 656–694], Parter and Wong [J. Sci. Comput., 6 (1991), pp. 129–157] and Wong [Numer. Math., 62 (1992), pp. 391–411, 413–437] for finite element discretizations.