It is hard to give a universal answer to the question but the best way is probably not to stay on the line "between TCP and UDP" but rather to go sideways :).
A bit more detailed explanation:
If an application needs to get a confirmation response for every piece of data it transmits then TCP is pretty much as fast as it gets (especially if your messages are much smaller than optimal MTU for your connection) and if you need to send periodic data that gets expired the moment you send it out then raw UDP is the best choice for many reasons but not particularly for speed as well.
Reliability is a more complex question, it is somewhat relative in both cases and it always depends on a specific application. For a simple example if you unplug the internet cable from your router then good luck keeping reliably delivering anything with TCP. And what even worse is that if you don't do something about it in your code then your OS will most likely just block your application for a couple of minutes before indicating an error and in many cases this delay is just not acceptable as well.
So the question with conventional network protocols is generally not really about speed or reliability but rather about convenience. It is about getting some features of TCP (automatic congestion control, automatic transmission unit size adjustment, automatic retransmission, basic connection management, ...) while also getting at least some of the important and useful features it misses (message boundaries - the most important one, connection quality monitoring, multiple streams within a connection, etc) and not having to implement it yourself.
From my point of view SCTP now looks like the best universal choice but it is not very popular and the only realistic way to reliably pass it across the Internet of today is still to wrap it inside UDP (probably using sctplib). It is also still a relatively basic and compact solution and for some applications it may still be not sufficient by itself.
As for the more advanced options, in some of the projects we used ZeroMQ and it worked just fine. This is a much more of a complete solution, not just a network protocol (under the hood it supports TCP, UDP, a couple of higher level protocols and some local IPC mechanisms to actually deliver messages). Since a couple of releases its initial developer has switched his attention to his new NanoMSG and currently the newest NNG libraries. It is not as thoroughly developed and tested and it is not very popular but someday it may change. If you don't mind the CPU overhead and some network bandwidth loss then some of the libraries might work for you. There are some other network-oriented message exchange libraries available as well.