In my experience, the cells which remain attached on the bottom of the flask are mostly living cells and do not undergo apoptosis yet. You may first verify this point, for example by a trypan blue test made on these attached cells or by any current fluorescent method, and then perform FACS analysis on floatting cells. Perhaps a time-dependent analysis made at different moments after the early appearance of floatting cells in your supernatants would give you more informations on the kinetics of apoptosis
Dominic is right. Adherent cells are usually alive since any dead ones would detach and disappear. The best strategy to analyze apoptosis would be to induce apoptosis using one of the commonly used apoptosis inducers (https://www.sigmaaldrich.com/life-science/cell-biology/cell-biology-products.html?TablePage=9560323) and then use the treated cells for Flow Cytometry. This way you can be sure that the manner of cell death you study is apoptosis and not one/a combination of the other forms of cell death.
After detaching by trypsin-EDTA, the adherent cells including many epithelial cells can be analyzed by flow cytometry for determination of apoptosis. Surely, PI or PI & Annexin V staining will help.
I would recommend using both, yes. It's very useful to get an accurate representation of what's happening to your cell population as a whole. The supernatant contains a mix of both dead and early/late apoptotic cells while the cells still adhering are mostly living but some might have initiated apoptosis. The caveat to this is you also end up getting a fair bit of apoptotic/dead cells in your no-condition controls.
maybe make a FACS for each kind of condition (attached and supernatant separately) to see debris, compensation and an idea about apoptotic values, and finaly take a sample of both for a FACS; but depends what u need to report; in another case directly use PI or ANEXINE V. Remember all in same condition and time.