Should it be on or off in order to get the best performance for BOINC?
I have one machine with a Intel i7 3930k and one with i7 3770k.

It depends on the project. I personally don't know, maybe others here can post what their experience is.
There is an active discussion over at PrimeGrid at Number Crunching/Double Top Secret Mystery Challenge indicating for the PG tasks except Sieve HT off provides the best performance there.
I know that Milkyway has a Hyperthread app that some users there have complain about it using all cores of the PC when it starts thus slowing down other projects running at the same time.