The correct differentiation between the lysogenic and lytic cycles is:
The host cell is destroyed during the lytic cycle.
In the lytic cycle, the virus takes over the host cell's machinery to replicate its own components, leading to the eventual destruction (lysis) of the host cell as new viral particles are released. In contrast, the lysogenic cycle involves the integration of viral DNA into the host genome, where it can be replicated along with the host's DNA without immediately destroying the host cell.