Go with bolts, and put a few spacers between the old joist and the new one. In short, you don't want the old and new joists touching because it's possible for the rot (in time) to xfer from the old to the new. I've used 2" x 4" x 4" PT blocks on either side of my bolts. Screw the blocks into the NEW joist with deck screws. I'm assuming you're working w/a PT deck.
My best to ya and hope this helps.
PS: You didn't ask about the 'ends' of the new joists and how they're to be attached to the face board (and the house). If you're OK w/that, fine. If not, post up on the Forum again.