This paper presents field measurement-based channel characterization for air-to-ground (A2G) and air-to- air (A2A) wireless communication systems using two drones equipped with lightweight software-defined radios. A correlation-based channel sounder is employed such that the transmitting drone broadcasts the sounding waveform with a pseudo-noise sequence and the receiving drone captures the sounding waveform together with the location information for the post-processing analysis. The path loss results demonstrate that the measurement and flat-earth two-ray results have similar trends for A2G while the measurement and free space path loss are similar to each other for A2A. The time delays between the direct path and multipath components are widely spread for A2A while the multipath components are mostly concentrated around the direct path for A2G generating a more challenging communication environment. We observe that the reflections from several buildings having metal roofs and claddings on the measurement site cause sudden peaks in the root-mean-square delay spread. The results indicate that the A2A channel has better characteristics than the A2G under similar mobility conditions.