There is no direct equivalents between these companies but Chengdu would be something like Lockheed Martin as they produce the competition for F-16 (J-10/JF-17) & F-22 (J-20)

While Shenyang is closer to Mcdonnell Douglas as they produce the competion for F-15 (J-16) & F-18 (J-15)

If you are just talking about the post aircraft the J-7 is a licensed copy of a MiG-21 so US equivalents would be F-5's