During a lytic cycle, the bacteriophage uses the replicative machinery of the bacterial cell to make many copies of its viral genome and to produce structural proteins of the phage head and tail. After phage DNA genomes are packaged into phage particles, the cell lyses (ruptures), releasing progeny phage capable of infecting other bacteria.
During a lysogenic cycle, the phage's DNA is inserted into the circular bacterial chromosome. The viral genome remains dormant in the bacterial chromosome, being replicated and passed to progeny bacteria along with host DNA sequences. When an appropriate extracelluar signal (e.g. environmental stress, UV light) impacts the bacterium, the viral plasmid genome is excised from the bacterial chromosome, and the phage initiates a typical lytic cycle.
So as far as which is more detrimental, the lytic will have a more immediate impact. However, over time it seems they both will eventually destroy the host.