Ill start from the end - having compared the coefficients, one would not talk of correlation (that is a different test - $Pearson's\ r$) since normally correlation is bivariate, meaning that no controls are affecting the relationship. One could say that drug A is more influential on the mortality of the bacteria, while controlling for drug B (or that it has a larger affect size).
Generally, when you wish to compare coefficients in a single model, than compare the $beta$ - or the standardized coefficients. In effect, if two coefficients have the same meaning and unit of measurement, that a direct comparison is possible.
Regarding comparison between models (with different bacteria mortality as your $\hat{Y}$, I would be more careful with the phrasing, because the situations are potentially different.
Example:
Say model 1 has $bacteria_1$ and model 2 has $Bacteria_2$ - both with survival percentage as the dependent variable, and both models have a $drugA$ coefficient. The models are:
$Bacteria_1=\beta_0+5X_{DrugA}$
$Bacteria_2=\beta_0+10X_{DrugA}$
You could say that every increase in 1% in the concentration of DrugA increases the death of Bacteria 1 by 5 percent, and that it increases the death of Bacteria 2 by 10 percent. But saying that it has twice the efficacy might be misleading. Perhaps Bacteria 1 is much more resistant to drugs than bacteria 2. If Bacteria 2 can be easily killed by drugs, than comparing efficiencies is difficult. You can say, however, that Drug A kills more of Bacteria 2 than Bacteria 1.
