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.

Related Questions

Are sulfacetamide sodium or monodox (doxycycline monohydrate) effective in treating acne scars?

Not for scars. This is not so much for treating scars as it for preventing scars by minimizing bacterial counts and the damage that is done by the bacteria and your bodies response tothe bacteria. Read more...
No. They are useful for treating acne, and treating it can prevent more scars. But these medicines won't actually do anything for existing scars. Read more...