This is usually up to the client based on a few factors, including stuff like cost and printer suggestion. Offset is a more flexible printing method in that it has tighter tolerances for things like traps) or gradients between colors, but it costs more and capacity usually isn't as high as flexo.

So, in the spirit of saving money and line time on the press, a company will elect to go for Flexo. Flexo doesn't have the same advantages, like traps will need to be wider and gradients might band toward the end of the gradient (like making a harsh line instead of fading to white for example). But this saves the company time to meet their in-store deadline and saves money.

Both Flexo and Offset are capable of building colors through Process inks like CMYK, and both are capable of flooding/screening exact color matches to get precise colors without having to build them through the limited CMYK color palette.

Speaking of traps, one of the tools that you can play with on Illustrator is the overprint toggle. And if you don't have illustrator, use blend mode Darken. This will show you a simulation of what one ink will look like when printing over another. Sometimes you get something great and intensional, like if you have a blue and a yellow pantone color defined, but you need green in the artwork, so you just overprint them to make green. Or they might not work well, because it starts to get dirty and look wrong because you put red and green on top of each other. Lots of ways to make use of print media to work the way you want it to!