The 2008 financial crisis and the subsequent recession had a significant impact on millennials and their money habits, even though many of today's twenty- and thirty-somethings were students when Lehman Brothers collapsed 10 years ago. A recent survey by Charles Schwab finds that 81 percent of those ages 16 to 25 watched their parents experience financial hardship following the 2008 financial crisis. And watching their parents struggle seems to have had a positive influence on millennials when it comes to how they save.

Millennials are more careful

Over 40 percent of millennials report setting aside money on a monthly basis, according to the Allianz Life Generations study. That's compared to 36 percent of Gen-Xers who report similar monthly savings. Allianz speculates that millennials are outperforming Gen X in part because they learned caution from observing their parents. "The Great Recession was, if anything, a nice 'reset button' to nudge up saving by younger people, which is quite useful, given the low saving rate in the United States," Kent Smetters, a finance professor at The Wharton School, tells CNBC Make It. Retirement savings is also a higher priority for many millennials. The same Allianz survey finds that 58 percent of them believe long-term saving is a basic necessity, ranking right up there with food and housing. And about half of millennials with a 401(k) say they contribute 10 percent or more each month. Only 36 percent of Gen-Xers say the same.

Those savings habits are particularly helpful for older millennials who themselves felt the effects of the 2008 financial crisis and subsequent recession. The St. Louis Fed found that those born in the 1980s are at risk of being the "lost generation" when it comes to building wealth. The level of wealth in 2016 among these households remained 34 percent below the estimated levels when compared to other generations' progress at that stage of life. "There's so much fodder and conversation about the adults that went through [the Great Recession], but no one's talking about the kids," Carrie Schwab-Pomerantz, a financial adviser, board chair and president of the Charles Schwab Foundation, tells CNBC Make It. The kids, it turns out, were taking notes.

Millennials are more conservative

Younger adults also tend to say that their parents tried to help them to become financially responsible — and, in the process, may have over-emphasized safety. A PNC survey earlier this year found that millennials' parents encouraged them to save rather than invest. About two-thirds of younger adults say their parents actively taught them to put money aside but only half say they were instructed to, or how to, enable their money to grow. Many millennials remain spooked by the market and reluctant to invest outside of workplace retirement accounts like 401(k)s. About 41 percent of millennials use a 401(k) or 403(b), according to a July Bank of the West study, but substantially fewer are willing to invest on their own. Less than a quarter have an individual retirement account, while only 12 percent use a brokerage account. The same survey finds that 65 percent of millennials say that living through the financial crisis made them more conservative with their money.