  We theoretically study the pulse-width dependence of the photoelectron
angular distribution (PAD) from the resonance-enhanced two-photon single
ionization of He by femtosecond ($\lesssim 20$ fs) extreme-ultraviolet pulses,
based on the time-dependent perturbation theory and simulations with the full
time-dependent Schr\"odinger equation. In particular, we focus on the
competition between resonant and nonresonant ionization paths, which leads to
the relative phase $\delta$ between the $S$ and $D$ wave packets distinct from
the corresponding scattering phase shift difference. When the spectrally
broadened pulse is resonant with an excited level, the competition varies with
pulse width, and, therefore, $\delta$ and the PAD also change with it. On the
other hand, when the Rydberg manifold is excited, $\delta$ and the PAD do not
much vary with the pulse width, except for the very short pulse regime.
