In absolute terms, Carlsen 2012 for sure is a stronger player than Kasparov 1985.
If Carlsen 2012 travelled in time played a match with Kasparov 1986, Carlsen would defeat Kasparov. This is simply because the technology-assisted preparation is a lot more efficient, and Carlsen has also an edge in opening theory, because he has the accumulated knowledge 1987-2012 that Kasparov does not have.
However, Kasparov is probably a stronger player than Carlsen. If we take the FIDE Top 100 List for June 2000 (the oldest one that can be obtained), we see that Kasparov with 2949 Elo competes with an average of 2641 for the 99 followers (Elo distance 208 points) while Calsen in Fide Top 100 for December 2012 with a 2048 Elo competes with an average of of 2702 for his 99 followers (Elo distance of 146 points).
Elo is about the difference of points, not about absolute values (100 points of difference for Elo mean that player A is 2 times better than player B, 200 points means 4 times better, and so on. So with that list, it meant that Kasparov was on average more than 4 times better than all his 99 followers, while Carlsen is probably less only 3 times better than the average of his 99 followers.
If we take the list were Kasparov has the maximum distance with his 99 followers and compare that distance with the best for Carlsen, we will be able to determine which player was actually the greatest, because with 99 data points, outliers (like another genius) get mitigate it.
I wonder however if Carlsen or Kasparov really care about who was better.
