Of course, there is some question as to when the Democratic Party actually came into existence. The Democrats themselves claim Thomas Jefferson as their founder, but the party he begat was called the Democratic-Republican Party. It became so dominant that its opposition, the Federalists, collapsed, leaving only various factions of the Dem-Reps to contest the election of 1824 against each other.
Nobody got a majority of votes in the Electoral College that year, so the House of Representatives decided the election by choosing John Quincy Adams. The chief loser, Andrew Jackson, was so outraged that he got together with Martin Van Buren and formed the Democratic Party for the purpose of contesting the election of 1828. Adams's faction was re-named the National Republicans, and the Democratic-Republican Party went out of existence. So, does the Democratic Party begin with the election of 1828, or the election of 1792?
Meanwhile, the Republican Party of today first contested a presidential election in 1856. That makes it a Grand Old Party indeed, though not as old as the Democrats. And as far as electoral success goes, the Republican Party not only has a higher winning percentage than the Democrats, it has won more presidential elections, in toto. If you count the Democratic-Republicans and the Democrats as a single political party, the Republican Party has the highest winning percentage of any major party contesting US presidential elections.
Counting Washington as a Federalist (he really was our only Independent President) and J.Q. Adams as a National Republican even when he was representing a faction of the Dem-Reps, we get the following won-lost stats for major political parties in US presidential elections.
Democratic-Republican Party, 6-3 = .667
Republican Party (GOP), 24-17 = .585
Dem-Rep/Democrat (if you consider them the same party), 28-29 = .491
Democratic Party, 22-26 = .458
Whig Party, 2-3 = .400
Federalist Party, 3-5 = .375
National Republicans, 1-2 = .333
Other, 0-19 = .000