We perform a comparative study for the quantum transport of telescoping carbon nanotubes, where the (5,5) and (10,10) nanotubes are coaxially aligned, using first-principles local-density-functional and tight-binding calculations. In both calculations, the intertube conductance initially increases as the hybridized length in the contact region increases, and then decreases, exhibiting a maximum conductance. However, the calculated conductances from first principles are generally smaller than those from the single pi-orbital tight-binding model. In the first-principles calculations, we obtain the maximum intertube conductance that does not exceed G(0) (=2e(2)/h), while individual tubes have two conducting channels, giving the conductance of 2G(0). On the other hand, the single pi-orbital tight-binding model gives the maximum conductance close to 2G(0), similar to previous calculations. Using a double-wall nanotube, we examine the effect of interwall interactions on conductance and find that the pi(*) states of the inner and outer tubes are strongly coupled in the tight-binding model, allowing for an extra conducting channel, while the pi(*) channel is closed in the first-principles calculations.