From personal experience, I have to say that wired devices use less power. Having Bluetooth enabled on my wireless devices drain them so quickly that I now avoid Bluetooth altogether.
Noting that this is only one sample by a user, an iPhone 5's battery capacity percentage (which supports Bluetooth 4.0) is shown here to lose 2.0-2.4% per hour playing audio through the headphone jack with Wi-Fi and Bluetooth off, and 2.6% with Wi-Fi and Bluetooth on. In comparison, playing audio over Bluetooth with Wi-Fi off consumed 3.4% of the battery capacity per hour.
These results are somewhat questionable, since the author claims that playing audio over Wi-Fi (with Bluetooth on) only consumes 2.4% per hour, similar to playing audio through the headphone jack, and less than playing audio over Bluetooth. It is well documented* that "Bluetooth is ... shown to be about 30% more energy efficient than WiFi to perform occupancy data transmission".
Still, this would be an easy thing to test with your hardware.
*Putra, G.D., et. al., 2017, Comparison of energy consumption in Wi-Fi and Bluetooth Communication in a Smart Building, Computing and Communication Workshop and Conference (CCWC), 2017 IEEE 7th Annual, Las Vegas