This paper presents comprehensive comparisons of the achievable throughput between the 32-/64-ary amplitude and phase shift keying (APSK) and cross 32QAM/square 64QAM schemes based on mutual information (MI) considering the peak-to-average power ratio (PAPR) of the modulated signal. As a PAPR criterion, we use a cubic metric (CM) that directly corresponds to the transmission back-off of a power amplifier. In the analysis, we present the best ring ratio for the 32 or 64APSK scheme from the viewpoint of minimizing the required received signal-to-noise power ratio (SNR) considering the CM that achieves the peak throughput, i.e., maximum error-free transmission rate. We show that the required received SNR considering the CM at the peak throughput is minimized with the number of rings of M =3 and 4 for 32-ary APSK and 64-asry APSK, respectively. Then, we show with the best ring ratios that the (4, 12, 16) 32APSK scheme with M =3 achieves a lower required received SNR considering the CM compared to that for the cross 32QAM scheme. Similarly, we show that the (4, 12, 20, 28) 64APSK scheme with M =4 achieves almost the same required received SNR considering the CM as that for the square 64QAM scheme.