Of course not always, but perhaps on average.
And of course there are many more ideologies and nuances than the binary choice "conservative vs. liberal" suggests.
As for the average, I'd say people on the "right-wing" are much more authoritarian than those on the "left-wing", with all that comes with it. They are less trusting, more fearful and easier afraid, or, positively worded, "more aware of risk and threat".
People on the "left-wing", on the other side, are much more trusting, not as easily scared, less aware of risk and threat, and thus very capable for cooperation. Both sides seem to be about even in numbers.
Both have their pros and cons, depending which traits are required in a given situation. But interesting enough, on the scale of entire peoples, both sides often enough don't change their attitudes, regardless of the situation society faces:
For example, when Hitler was about conquering world dominance and murdering hundreds of millions of people, very trusting and risk-unaware left-wing pacifists were still protesting for peace in America. Although the situation very obviously was very risky and required urgent response.
Likewise, even in situations when risks are minimal, and the best and most promising course of action would be trust, cooperation and compromise, because risks are low, the right-wingers are still wetting their pants, exaggerate the minimal risk, and destroy opportunities with their distrust. Perhaps even call for waging stupid wars.
It looks like over the course of history, a society needs both sides to be able to deal with the different kinds of challenges it faces. Sometimes it's one side, sometimes the other. If one of both was missing in a given situation, a society could get into real trouble.