QPSK vs. 4-QAM?

I am wondering if there are any differences in the BER performance of QPSK and 2 amplitude, non-rectangular 4-QAM, when the minimum distance between signal points is the same for each constellation. From what I read, the performance of the two are the same. The average energy per bit in each signal constellations are the same. But when I do a Monte-Carlo analysis, it turns out that 4-QAM has a slightly higher BER (by about 2dB). Each system is simulated using the same SNR/bit.

Thanks in advance,