actually, I think it's not so much who it helps as who it hurts which I think is the C's simply because the C's have continually shown that having extra time between games results in them playing worse than usual.
C's have been really good with extra rest this year. They've been bad in back to backs and other short rest situations (largely driven by Horfords performance)
5-8 (.385) with 0 days off
32-19 (.627) with 1 day off
9-4 (.692) with 2 days off
2-2 (.500) with 3+ days off
2 days off does seem to be the sweet spot, but then there's the 3+ days off (with minimal data, I know).
Personally, when I think of extra rest, I think more like a week off, and then I think about how the C's were 0-4 after the All-Star break this year. Then I think about last year when they came back from England. I really thought having that rare mid-January break where they had 1 game in 10 days would do wonders for the team, why wouldn't they come back rejuvenated from that? 0-4 there too. Of course they did come out of last year's All-Star break 4-0 (to all non playoff teams though). Not a lot of examples, but those are what comes to mind when I think about extra rest, not your typical 1-3 days off.
Not too worried about regular season results though. C's often played down to inferior competition, but always seemed to bring it against top talent. It's the playoffs, and with how banged up everybody is, I don't see how this extra rest could be anything but a good thing.