From my understanding, it would essentially do the same thing. When you burn steem, it will simply be re-printed in upcoming reward periods because the rate of inflation is already set. In other words, by the end of the year there will be the same amount of steem whether some is burned or not. Every time steem is burned, the amount of steem created per day goes up slightly to keep the inflation rate the same.

I don't know for sure but I think that declining rewards goes back immediately to today's reward pool to be split between everyone else while burning would just go be reprinted over time thereby giving the witnesses and stakeholders a percentage of the new steem.

Hopefully that makes sense. Upvoted for visability.