The Federal Reserve is grappling with cooling down a searing-hot labor market, and aggressive rate hikes will ultimately send the US economy into a deeper recession than what Europe will face, according to Bank of America. 

Because Europe had a less rapid recovery from the pandemic than the US, Europe's GDP has less room to decline, BofA said, adding that the eurozone still hasn't fully recovered from the recession..

"Europe does not need to cool off its labor market to get inflation down," analysts wrote in a note Friday. "By contrast, the Fed has to do the dirty work of bringing labor demand down and in line with labor supply. Adding to the challenge is the fact that pent-up demand for labor in the US is making it very hard to cool off the labor market. So the Fed has to deal with both the risk of second-round effects and the first-round effect of an overheating labor market."

The strength of the US labor market was on display Friday, when the Labor Department reported nonfarm payrolls skyrocketed by 261,000 in October, above expectations, while unemployment surged to 3.7%, above the expected 3.5%. 

BofA analysts said the US economy is "clearly overheating,"

 The jobs data could push the Fed to continue with its aggressive rate hikes, even after it made its fourth consecutive 75-basis-point increase on Wednesday. The fed fund rate now stands at 3.75% to 4%.

"If the Fed wants to get labor cost inflation under control in a timely manner, we think it needs to engineer about a 2% rise in the unemployment rate," the note said.

Europe currently faces significant downside risks that could change the outlook, such as the prospect of further natural gas supply cuts from Russia and uncertainty from upcoming sanctions on Russian oil.  

"We can't rule out additional shocks to the energy market, due to additional supply disruptions," BofA said. "Europe is vulnerable to confidence shocks if the war in Ukraine escalates. And Europe is quite vulnerable to a colder-than-normal winter."