FRANKFURT—Worried about the depth of its economic downturn, Europe is rapidly narrowing the gap with the U.S. in its crisis reaction, lining up two new packages probably value hundreds of billions of euros that reflect classes figured out in former crises and boost prospective buyers for a world-wide recovery.

Early in the coronavirus pandemic, the U.S. and Europe diverged drastically in the quantity of firepower each individual threw at an economic crisis that threatens to be the worst in a long time. The Federal Reserve and the U.S. Treasury have been…