From a roster standpoint, the 2013 team easily. The problem is that while you mention they rallied after Rondo went down, even then, that team underperformed.
So it's very hard for me to say one way or another, considering how they played the 2015 team would take them, but considering how they should've played then 2013 should take it.
The first and major error of 2013 was having Bradley play PG for us. So that's a coaching error, so it can't be excused and fits under the parameters of what a coach brings to the table. When Rondo went down, we were bringing the ball up by committee, we were passing the ball forward to whomever was available for early offense opportunities. Then after 6-7 games of that working beautifully, Rivers decided to give the keys to Bradley as the sole PG, he stopped running the floor, instead going back to get the ball. And we all know how he sucks as a PG, and then his defense became mediocre during the playoffs in part because of his worries on offense.
Then you have Doc Rivers benching Courtney Lee even though after the first couple of months, in which he struggled, he was having his most efficient season to date, and we saw how he continued that on the following seasons.
Then you have Rivers over-playing Jason Terry. Enough said on that.
I don't recall the health situation though.
Anyways, given all the facts, even though that 2013 roster should've been that much better, I'll say the 2015 takes them. In fact, the 2013 should've been the best if not one of the best teams we fielded in the Pierce-KG era, it became a disaster... mainly because of Doc Rivers doing his worst coaching job of his career.
Funny thing about 2013 was Ainge trading Collins away just so Doc would stop playing him, though Crawford eventually got us some value.