Does that mean that there`s apoptosis where an increase is found (in the means of western blot after treating ) and vice versa? Or can I speculate that the decrease is due to cellular resistance against apoptosis?
a decrease in monomeric Bax band could mean either oligomerization to increase glycolysis or cleaved to p18 form to damage mitochondria for apoptosis. See my paper
Basically I think that your idea is correct: the BAX increase means that apoptosis is being induced. But I am not that sure that a decrease in BAX means resistance.
I think that you need to check if the decrease in BAX is accompanied by a decerase in apoptosis. Remember that there might be other apoptosis pathways independent from the BAX- mitochondrial-caspase pathway.
In my opinion, before reaching to any conclusion first you should at least check the effect of your test compound on apoptosis (e.g., Annexin V-PI staining) using both kind of tumor cells. The increase in Bax can be correlated with induction of apoptosis, but you are advised to again confirm whether your compound really decreasing Bax levels in other cells?
As others already suggested you may want to interrogate your cells a little further. If you've done westerns for the Bax stain, you might as well check Bak, and other BCL-2 family members to give you a bigger picture. Also cleaved PARP or caspase 3 might be helpful. Or otherwise definitely any apoptosis assay to verify a correlation between your observed phenomena and apoptosis.