Tinnitus does not sound like crickets... it is a continuous high pitched ringing sound in the ears. The Om vibration on the other hand can sound like crickets, sometimes being very loud, and it can be heard 24/7. The Om vibration (Omkara nada) can take many different forms as different stages of the purification process happen. Personally I have never found it disturbing... and it doesn't last forever.
Just an add on from my knowledge bank, that tinnitus has no specific sound. It can be any sound, any pitch and with different volume of different sounds at different times. You can have a high pitch constant tone together with a more or less constant lower bubbling sound like a flushing toilet simultaneously, for example, or several different pitches ringing at the same time... It all depends on which hairs has been damaged inside the cochlea.
*just had my tinnitus checked in an advanced machine and got every Hertz identified and pointed out*