Are tobramycin drops or sulfacetamide sodium drops more effective in treating conjunctivitis?

Same: Both can be used to treat conjunctivitis, but ophthalmologist don't use these as often as primary care and emergency medicine providers.

Antibiotics: Antibiotics are selected based on their spectrum of bacterial infection coverage. The one that eradicates the infection is the correct antibiotic. An antibiotic can be selected more accurately if a culture is taken and the results of the culture can be used to tailor the correct antibiotic choice.