Security and privacy
AirDrop uses TLS encryption over a direct Apple-created peer-to-peer Wi-Fi connection for transferring files.[13] The Wi-Fi radios of the source and target devices communicate directly without using an Internet connection or Wi-Fi Access Point.[13]
from:
https://en.wikipedia.org/wiki/AirDrop
In my opinion, you are likely seeing the effects of the Mac Pro taking longer to set up its Ad-hoc Wi-Fi network, or reluctance to use advanced Wi-FI sending such as multiple antennas to produce really fast speeds. The Mac Pro 2013 models the oldest Mac Pro that can offer this support at all -- previous Mac Pro can't do it. Along with Handoff and similar services, initial negotiation appears to require Bluetooth LE 4.0, which just appeared on that Mac, and my be somehow inferior in its first implementation there.
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That said, if you are genuinely concerned about transfer speeds in this situation, you should use File Sharing, and if those speeds are still not adequate, get off Wi-Fi and onto Ethernet for better speeds and less interference from other devices in you Network Neighborhood.
