Magnus Carlsen is going to be an all time great in our history books. Potentially, even better than Fischer was.
"Greater" is a different question, more one for sports fans than sports scientists. What do you need to be great at a sporting vocation? Pure playing strength? Longevity? If so, in years, or in number of championship matches won? Dominance over your peers? Cultural impact on the world outside of your sport? Some kind of adjusted playing strength where we hypothesize how strong players would be given all the same opportunities and training material? If so, should it be modern grandmaster games and engines, or that from an earlier era?
"All of the above" is a good answer, and depending how you weight them you could incontrovertibly claim any of Carlsen, or Kasparov, or Fischer is the "greatest". You could also try to squeeze out a case for Morphy, or Lasker, or Capablanca.
You can't compare the best in a given era because the players now learnt from the players in that era i.e. Carlsen grew up studying Kasparovs games so it's simply a flawed comparison.
Instead he suggests a metric of "how far ahead of the field" they where, So Morphy and Fischer do really well on that metric, Kasparov does as well, Lasker and most of the other greats.
Fischer was unique in so many ways but late 1980's Kasparov would have crushed him.
Carlsen may be the only player to have a reasonable claim to be his equal.
There is still advantage in preparing the information in a way it's useful/easier to remember and that's what the teams of top GMs do but there are no purely chess secrets anymore. It's just much harder to be ahead of the field today.