From the peak to average power ratio point of view OQPSK is better than pi/4-DQPSK. What is the advantage of pi/4-DQPSK compare to OQPSK? Why Bluetooth 2 use pi/4-DQPSK instead of OQPSK?
One particular advantage of pi/4 QPSK and pi/4 DQPSK is that there is always a transition between symbols, making demodulation simpler. Differential - PSK (such as DQPSK) can be demodulated without a local oscillator (by comparing previous symbols to the current ones), making for extremely low cost receivers at a modest expense in performance (sensitivity).