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's cellular machinery to replicate itself, ultimately leading to the lysis (destruction) of the host cell and the release of new viral particles. In contrast, during the lysogenic cycle, the viral DNA is integrated into the host's genome and can remain dormant without destroying the host cell until it eventually enters the lytic cycle.