We report the large-signal performance of high electron mobility transistors (HEMTs) fabricated on GaN- and AlN-capped AlInN/GaN epilayers grown on semi-insulating SiC substrates. Large-signal measurements at 10 and 40 GHz are presented with both gate and drain dynamic loadlines to clarify the factors limiting the high-power performance. Devices fabricated with AlN-capped epilayers show a marginal advantage in terms of higher current and reduced dispersion, but GaN-capped epilayers perform better in terms of reduced short-channel effects and better channel control. In large-signal operation at 40 GHz, both device types delivered power densities in excess of 4.5 W/mm. A maximum power density of 5.8 W/mm is achieved on GaN-capped devices which is, to the best of our knowledge, the highest power density reported at 40 GHz in AlInN/GaN-based HEMTs.