The Russian national flag flaps in the wind on Oct. 9, 2014 in Sochi, Russia. (Photo by Mark Thompson/Getty Images)

Russian President Vladimir Putin, President Obama and politicians in both countries have been trading barbs for months as the countries' relations have plunged ever southward.

But what about the countries' citizens? Are they as at odds as their leaders' rhetoric suggests?

WorldViews delved into recent opinion polls conducted by the Pew Research Center and Gallup. Together, the data provide interesting insights into what Russians and Americans think about each other and themselves, how they differ in certain ways, and how they are similar when it comes to other aspects.

Ways Americans and Russians think differently

Less than half of all Russians think the U.S. government respects personal freedoms -- 20 percent fewer than last year. It is interesting to note that only one year ago, Russians and Americans had a similar opinion about the U.S. government's respect for personal freedoms. The massive decline since then has coincided with the upheaval in Ukraine, as well as revelations about NSA spying programs abroad.

While trust in the U.S. has also declined in other countries, the majority of respondents worldwide -- 58% -- think that the U.S. government respects the personal freedoms of its people. That's more than twice as many as who believed the same of Russia.

Russians' and Americans' views of the other country are  more negative today than any time in the past 10 years.

The public in each country also differs in another significant way: How they view their leaders. In Russia, Putin's popularity has soared, while the U.S. public has grown increasingly weary of President Obama.

Russian President Vladimir Putin. (ALEXEY DRUZHININ/AFP via Getty Images), US President Barack Obama (SAUL LOEB/AFP via Getty Images.)

Putin's strong approval ratings have been linked to Russians' enthusiasm about the country's military actions in Ukraine. However, such support might be fragile in the long run: The same poll found that satisfaction with life is about 20 percent lower among Russians than among Americans.

Russians are also much more likely than Americans to believe that one needs to be lucky to get ahead in life.

While many Russians think they need to be lucky to achieve their goals, nearly half do not believe they would have to live in a free market economy in order to do so.

There are also some key gaps when it comes to social values, such as approval of homosexuality.

The fact that Russians are more likely than Americans to find drinking morally unacceptable might surprise those aware of Russia's love for vodka, though.

(Photos: Pernod Ricard via Bloomberg News)

Ways Americans and Russians think similarly

But social issues are also where Americans and Russians seems to share the most common ground. On some, Americans and Russians are actually closer to each other than they are to populations in many other countries in the world.