I'm not tptacek, but...
After lightly reading through both books, I think Gray Hat Python is a great book for more advanced security concepts, especially on the reverse engineering and exploit dev side of things, but isn't a very good book for learning Python or programming.
Violent Python on the other hand is a great book for beginners to Python and programming, and it teaches both pretty well, but it only goes into surface level security concepts for the most part.
Gray Hat Python is closer to a Windows API/x86 assembly book than a Python one. Violent Python is a real Python book and mostly covers general information security and network security concepts.
Gray Hat Python is also purely application security. Debugging, reversing, hooking, writing shellcode, exploiting... Violent Python is almost entirely network security, with one chapter on forensics. Exploit dev vs. exploit user.
It depends on your experience level and what you want to actually learn. If someone was brand new to Python, application security, and even programming, I'd recommend reading Violent Python first and then Gray Hat. If someone has more advanced security knowledge and has some decent programming skills already, I'd probably tell them to skip Violent Python.
Or if they wanted to focus on appsec vs. netsec, I'd direct them to one or the other based on that. If you want both, you should definitely read both.