Yawn, cherrypick starting dates and you can conclude anything. Start from 1968 and it's Republicans who have the upper hand... or go back to 1960 to make it Democrats again... or 1952 for Republicans again... or 1932 for Democrats again... and so on.
I am aware that dates can be used to draw one's own conclusion. If you looked at the three presidential elections in the 1980's you'd think that the Democratic party didn't exist.
Still, political eras are a real thing, and most political scientists can look back and determine periods of time when one party had the upper hand.
1) fifth party system: FDR's election created the new deal coalition. From 1932 to 1967 the Republicans only won 2 presidential elections.
2) sixth party system: There is debate as to when it ended, or if it has ended at all, but most agree it started in 1968 with the election of Richard Nixon. I personally believe that this era ended in 1992. Between 1969 and 1991, the Republicans won five presidential elections out of six. That's definitely a trend.
3) I don't know if you can call this a new era or a transition period, but since 1992, it's become increasingly more difficult for Republicans to win presidential elections, while it's become easier to win control of congress.
-since 1992, the democratic candidate's electoral vote total has never fallen below 251, while the republicans electoral total has never risen above 300. The GOP actually received less than 200 EV's in three out of the last 5 elections. That is most certainly a trend.