Cricket is older, the first definite mention of the game is found in a 1598 court case concerning an ownership dispute over a plot of common land in Guildford, Surrey. A 59-year old coroner, John Derrick, testified that he and his school friends had played creckett on the site fifty years earlier when they attended the Free School. Derrick's account proves beyond reasonable doubt that the game was being played in Surrey circa 1550, the first published account of baseball wasn't untill 1744 where a publication in England by children's publisher John Newbery called A Little Pretty Pocket-Book includes a woodcut and a rhyme entitled "Base-ball." There were older games that can be seen as precursers to both games.
If you want the modern versions of the game, the first international cricket match was played in 1844 while the first official game of baseball played with codified rules was 19th June 1846.
Edit: I disagree with Binga, the two games are mutually exclusive. Baseball didn't stem from cricket both games come from similar early games like La soule, a french game that dates back as far as the 1300s and Stoolball, an English game of the 1500s, both appear to be precursors for both Cricket and Baseball as they share similar characteristics.