TCP is often prioritized over UDP traffic. If you can build a simple reliable protocol over UDP, it'll be easier in the long run, especially with NAT negotiation, and not having to deal with multiple sockets.

Building a reliable in-order messaging system on top of UDP isn't that hard, and you can keep it simple, if you don't care about latency (your messages arriving a few fraction of a second later). And in general, you will already have some sort of protocol to establish and maintain connectivity with your clients, which would roughly mimic a TCP-IP state machine.