Hyper Threading is Intel's technology that enables processors to implement more threads. So for example, the current desktop i5 processors have one thread per core. i3 and i7 processors have the ability to implement HT which allows for two threads per core. HT can be beneficial depending if the software is designed to use it. If the software is not designed to use HT, only one thread will be used to perform tasks. If the software is designed to use HT, two threads will be used to perform tasks thus greater performance. Most games aren't designed/coded to use HT. There are a few that do use it but unless you play those games exclusively, the benefits of HT aren't relevant.
More in depth explanation:
http://en.wikipedia.org/wiki/Hyper-threading
I haven't read about the 780ti issues you speak of so I can't comment on that. I can say that an i5-4670k can support a 780 ti no problems.
As for the difference between the 2011 and the 1150 socket, there are even less games that need the 2011 socket than there are games that support HT. For gaming, the added bonus' don't add up unless you're doing something like 6 screens and 4 GPUs. That's when the more powerful CPU (like an Intel 6 core) might be needed. IMO, the return on the investment isn't worth it. 2011 socket is pretty expensive.