Should I use activity or activities

This is a matter of preference. Activity is one of those odd nouns which is singular but can stand in for a plural. "We are tracking his activity" and "We are tracking his activities" are very close, but the latter implies tracking the individual granular components of his overall activity rather than his general status.

I would lean towards "activity" because you are trying to make a global statement about a property of the drugs rather than a low-level pinpoint analysis.

The sentence might trip up a reader either way, so I might suggest a rearrangement:

"Each drug has identical antibacterial activity."

In fact, "activities" would be perfectly legal there too, but with the same implication. "Activities" makes the reader think of the individual strands and how they map up perfectly with one another, which is not important here.