Tradeoffs between QPSK and BPSK re. spectral efficiency, error rate, etc
Assuming reasonable SNR (>10 dB), QPSK will double your data rate, but the error rate is similar since the two phases of QPSK are independent. Specifically BER at the same Eb/No is the same. Since there are 3x the number bits, Eb is 3 dB worse.

In general use pi/4-QPSK or OQPSK instead of QPSK.