In the present (as of 11/6/2019) political climate, with a Democratic House of Representatives getting ready to impeach a Republican president, this is a particularly difficult question to answer. Levels of bipartisanship are at record lows in the American political system, with more clear blue water between the political parties than ever before. Under such circumstances, it's difficult to detect any real similarities between Democrats and Republicans.
Nevertheless, and speaking in the broadest possible terms, one could argue that the two parties have similar, if not identical, long-term goals but differ radically in how to achieve them. For instance, both Democrats and Republicans want the United States to be a prosperous country. However, whereas Democrats favor more government intervention in the economy to bring about this particular goal, Republicans opt for a more hands-off approach, arguing that prosperity comes through government getting out of the way and allowing businesses to make their own decisions wherever possible.
Continuing with the economic theme, one could also say that Democrats and Republicans alike are generally supportive of a capitalist economy. Though a handful of prominent Democrats, such as Representative Alexandria Ocasio-Cortez, are avowed socialists, most Democrats remain committed to the capitalist system, albeit one that is dramatically reformed to operate more effectively for working people.
Traditionally the party of big business, the Republicans are also wedded to the capitalist system, which they regard as being the best means of achieving prosperity. However, even some Republicans have argued that the current system doesn't work effectively, which is why they've put forward proposals that establish tariffs on some imported goods, especially from China, as a way of protecting American jobs and businesses.
Though such proposals may differ from those of the Democrats in terms of substance, they nonetheless share with the Democrats an impatience at how capitalism has developed, especially in relation to its impact on American workers.