You get what YOU agreed upon / negotiated, not what others agreed upon / negotiated.
It is good practice before you say, "Yes, bump me!" to ask them what they are offering and if they can confirm you on the next available flight.

Never, never take the free ticket (unless that is the only thing they are offering... in which case still ask for the Credit Voucher, they may give it to you).

(I know the below is true for NW, not sure of other airlines)
You don't earn miles on the free ticket.
Free tickets come from the same class as award flights, so they can be hard to book.