Morse code was invented by an American called Samuel Finley Breese Morse, (1791-1872). He was not only an inventor but also a famous painter. The SMS (Short Message Service) concept was first developed in the Franco-German GSM cooperation in 1984 by Friedhelm Hillebrand and Bernard Ghillebaert. The first text message was sent years later on December 3rd, 1992 from Neil Papworth, a former developer at Sema Group Telecoms.
Here is a competition video between the two technologies, watch to see which one wins!