  In this paper we compare approximation properties of degree $p$ spline spaces
with different numbers of continuous derivatives. We prove that, for a given
space dimension, $\smooth {p-1}$ splines provide better a priori error bounds
for the approximation of functions in $H^{p+1}(0,1)$. Our result holds for all
practically interesting cases when comparing $\smooth {p-1}$ splines with
$\smooth {-1}$ (discontinuous) splines. When comparing $\smooth {p-1}$ splines
with $\smooth 0$ splines our proof covers almost all cases for $p\ge 3$, but we
can not conclude anything for $p=2$. The results are generalized to the
approximation of functions in $H^{q+1}(0,1)$ for $q<p$, to broken Sobolev
spaces and to tensor product spaces.
