We have fabricated InxAl1-xAs/InxGa1-xAs metamorphic high electron mobility transistors (MHEMTs) with x=0.36, 0.43, and 0.53 on GaAs, and lattice-matched (LM) HEMTs with x=0.53 on InP. Using the HEMTs, we have carried out systematic studies on the electron velocity and the impact ionization in the InGaAs channels with several indium contents. The electron velocity is determined by the gate length dependence of cut-off frequency. Although high-density crystalline defects propagate into the channels of the MHEMTs, the electron velocity is not affected by the defects. Impact ionization phenomena, which dominate on-state breakdown voltage, have been investigated by gate-current analysis in the prebreakdown regime of the HEMTs. We have estimated the characteristic electric field of the impact ionization for InGaAs. It has been found that the gate current due to the impact ionization of the MHEMT with x=0.53 is smaller than that of the LMHEMT, which is explained by the enhanced electron-hole recombination by the crystalline defects in the MHEMT.