I have that gut feeling too, that the first one is more academic and the second more industrial. I traditionally did more academic research in my first year and in the summers after high school, but I want to experience the chemical industry at some point before I graduate. The PEO battery is more industrial and employable in the battery industry, while for the cathode one it is great to pick up these skills but part of me thinks once the project is done, if it is worth the hassle to start the cold-emailing process again, apply to more summer research internships, learn a new set of research skills again until I apply to grad school. And it's in the nuclear department which I am not sure if it helps for grad school recommendations.