If all I'd had for inspiration when learning the game was some bats##t-boring endgame trudger like Carlsen, I wouldn't have bothered with it. Morphy all the way.
Anyone trying Tolstoy instead of Tolkien at 12 might conclude that Tolkien is the better author of the two since he is more accessible. But one can appreciate both, it isn't just that one of them takes more effort and because of this must be worse.
Carlsen's games are certainly more advanced than many "fun" games involving much weaker players, but he is far from some "only boring endgames"-player. Just a quick look at this year results in many highy entertaining games like these:
http://www.chessgames.com/perl/chessgame?gid=1721543
http://www.chessgames.com/perl/chessgame?gid=1721397
http://www.chessgames.com/perl/chessgame?gid=1704802
http://www.chessgames.com/perl/chessgame?gid=1713205
http://www.chessgames.com/perl/chessgame?gid=1717640
http://www.chessgames.com/perl/chessgame?gid=1713231
http://www.chessgames.com/perl/chessgame?gid=1713491
Morphy's games are obviously more accessible since the level of the games is much lower. At the same time, Carlsen scored 5-0 in just over a year against the reigning World Champion, and three of those games were won in 30 moves or less. It isn't as easy today to just sac, sac and mate as in Morphy's day, but Carlsen has some very exciting games, and has even played the King's Gambit in a top tournament, the only elite player for decades to do that in classical chess. So I don't find him all that boring, even if few amateurs of course would appreciate a Carlsen game as much as Morphy vs the Duke & the Count.
Morphy games are way more fun and accessible (at least for me) so in that sense of "better" I vote for Morphy
If fun and accessible equals better I'd vote for most 2000 rated players as better than Carlsen :-)