I agree with pitot. Whether or not they carry their service
revolver depends on their department within the CNB, but if you're
a frontliner most definitely you will carry your revolver with you
almost all of the time.
Their training is actually with police officer/senior police
officer trainees, ie either 6 months [cpl/sgt] or 9 months
[inspector/asp]. Learn the same thing, with a bit extra thrown
in.
Legal powers is different also. Police are empowered to enforce all
laws under the sun. CNB's powers is more to misuse of drugs
act-related offences. They have a lot of powers relating to the
said act. In fact, more than the police.
But of course, if a robbery has taken place, they can detain the
perpetrator. But the arresting party and subsequent in-charge case
will be the Police.
And yeap, their working hours are irregular, cos you'll never know
when they will be conducting operations. They are a very, very,
very secretive bunch. But for a good reason lah. 
For your last comment, perhaps they are similar to the CID in terms
of:
1) no need for uniforms
2) can carry service revolver back [depends on department,
though]
3) irregular hours, but only when there is impending major
operation.
but then police also like that lah.
