Both

Really. My answer will be subjective, because I "reenacted" postapo trader in a postapo world few times. So I have some experience.

Both are edible

As perfectly explained by another answer I've already upvoted. Both are also relatively easy to farm.

And both are tasty. They really are, once you give it a try!

There is no food worse than boring food

If you live for few days on scrambled eggs and chicken meat, deep fried roach is some very welcome diversity. If you try to eat dried nutrients, you start to crave something normal. If you work for 12-16h / day, you need protein. And so on.

Safety from disease

If bird flu kills all your chicken, you have roaches. And vice versa. Much less risk of losing it all.

Leftover disposal

Cannibalism is not healthy for your animals. But by feeding chicken leftovers (fresh!) to roaches, and roaches to chickens, you increase your risk only marginally, and save quite a lot of organic matter.