Both

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

Both are edible

As perfectly explained by another answer I already upvoted. And both are relatively easy to farm.

And both are tasty. Really are, once you really 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 very welcome diversity. If you try to eat dried nutrients, you start to carve for 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 feeding chicken leftovers (fresh!) to roaches, and roaches to chickens, you increase risk only marginally, and save quite a lot of organic matter.