The most accurate way to differentiate between the lysogenic and lytic cycles is:
The host cell is destroyed during the lytic cycle.
In the lytic cycle, after the virus replicates and assembles new viral particles, the host cell eventually bursts (lyses), releasing the new viruses. In contrast, during the lysogenic cycle, the viral DNA integrates into the host cell's genome and does not immediately destroy the host; instead, the viral DNA is replicated along with the host cell's DNA when the cell divides, and the virus may enter the lytic cycle later under certain conditions.