Understanding of recombination and photoconductivity dynamics of photogenerated charge carriers in GaxIn1-xP NWs is essential for their optoelectronic applications. In this letter, we have studied a series of GaxIn1-xP NWs with varied Ga composition. Time-resolved photoinduced luminescence, femtosecond transient absorption, and time-resolved THz transmission measurements were performed to assess radiative and nonradiative recombination and photoconductivity dynamics of photogenerated charges in the NWs. We conclude that radiative recombination dynamics is limited by hole trapping, whereas electrons are highly mobile until they recombine nonradiatively. We also resolve gradual decrease of mobility of photogenerated electrons assigned to electron trapping and detrapping in a distribution of trap states. We identify that the nonradiative recombination of charges is much slower than the decay of the photoluminescence signal. Further, we conclude that trapping of both electrons and holes as well as nonradiative recombination become faster with increasing Ga composition in GaxIn1-xP NWs. We have estimated early time electron mobility in GaxIn1-xP NWs and found it to be strongly dependent on Ga composition due to the contribution of electrons in the X-valley.