  The constraints on the $\Lambda$CDM model from type Ia supernova (SNe Ia)
data alone and BAO data alone are similar, so it is worthwhile to compare their
constraints on the property of dark energy. We apply the SNLS3 compilation of
472 SNe Ia data, the baryon acoustic oscillation measurement of distance, the
cosmic microwave background radiation data from the WMAP7, and the Hubble
parameter data to study the effect of their different combinations on the
fittings of cosmological parameters in the modified holographic dark energy
model and the Chevallier-Polarski-Linder model. Neither BAO nor WMAP7 data
alone give good constraint on the equation of state parameter of dark energy,
but both WMAP7 data and BAO data help SNe Ia data break the degeneracies among
the model parameters, hence tighten the constraint on the variation of equation
of state parameter $w_a$, and WMAP7 data do the job a little better. Although
BAO and WMAP7 data provide reasonably good constraints on $\Omega_m$ and
$\Omega_k$, they are not able to constrain the dynamics of dark energy. On the
other hand, SNe Ia data do not provide good constraints on $\Omega_m$ and
$\Omega_k$, but they provide good constraint on the dynamics of dark energy,
especially the variation of the equation of state parameter of dark energy, so
we need to combine SNe Ia with BAO and WMAP7 data to probe the property of dark
energy. The addition of $H(z)$ data helps better constrain the geometry of the
Universe $\Omega_k$ and the property of dark energy. For the SNLS SNe Ia data,
the nuisance parameters $\alpha$ and $\beta$ are consistent for all different
combinations of the above data, and their impacts on the fittings of
cosmological parameters are minimal. By fitting the data to different models,
$\Lambda$CDM model is still consistent with all the observational data.
