If you have 1 value for each sample (culture) then one of the two methods you mentioned would be applicable, if not you should look for other ways (I suggest repeated measures one way ANOVA).
Assuming only 1 value for each sample: Kruskal-Wallis tends to have less power than an ANOVA if the population follows assumptions of normality and are homogenous (power is around 95% of that of ANOVA). If however your populations might be somewhat skewed and/or non-normal then Kruskal-Wallis have the same or better power compared to ANOVA.
In the case of cell cultures I'd say you can assume normality and therefore go with a regular ANOVA.
If you get a significant result on the ANOVA you can then use a Tukey test with unequal sample sizes to find out which group(s) differ from the rest.