Lots of people are drawing parallels but there are huge differences. During the Black Death the church was responsible for burying and saying prayers for the dead. Many people bequeathed money for good causes which funded the building of many churches in the decades that followed. This included many new Cathedrals north of the Rhine and a shift away from Latin to vernacular languages.
It also provided funds for science and technology, providing the world with spectacles, gunpowder, printing and compasses. Gunpowder put an end to siege warfare and made battles more mobile and lethal. Accurate compasses encouraged the age of discovery.
Printing allowed cheaper books, so literacy rose. It also allowed the spread of new ideas from science to politics as of faith so helped fuel the Reformation and democracy.
The Black Death put an end to the decorated gothic style of architecture and art. The labour intensive ornate designs were followed by perpendicular gothic, pared down to become the go to style for English churches.
In England the post-plague fall in population caused a rise in demand for labourers who demanded better conditions so King John grudgingly signed Magna Carta. In Europe the pope allowed the introduction of African slaves as long as they were non Christian, so paved the way for the Atlantic slave trade.
The biggest difference between he two periods has to be that of resources. Historically most energy came from renewables: wind, water, timber so recovery was often limited by manpower. We are in an age of diminishing resources so the recovery is a harder call.