I don't think you can say that QAM is "better" than, say PSK. QAM modulates amplitude as well as phase, so it is more spectrally efficient (measured in bits/sec/Hz). In a given channel width, QAM can send more bits/sec. But you pay a price in the required signal to noise ratio (as Shannon's equation tells us). So if you want a robust channel, PSK would be better.
Another advantage of PSK over QAM is transmitter efficiency. If you use QAM, the transmitter cannot operate at max power all of the time. When the amplitude of the QAM symbol is less than maximum, you have to transmit that symbol at less that maximum transmitter power. Instead, if all you are modulating is the phase of a symbol, the transmitter can always be operating at peak power, and the transmitted signal will always be at maximum strength. Which is why PSK is often preferred for long range communications such as satellite links.
As to Jake vs Dent models, they are used to model Rayleigh fading for moving vehicles, where you experience Doppler shift.
In digital modulation, minimum distance (d-min) between two adjacent symbols can affect the bit error rate (BER). In other words, increasing d-min will lower the BER.
M-QAM has smaller d-min than M-PSK for M > 4 and same transmitted power. In case M = 2 and 4, QAM and PSK have exactly performance.
In conclusion, M-QAM can provide better BER performance over M-PSK.
I recommend you to read chapter three in Digital communication, Proakis