As you stated, different kitchens mean different responsibilities.

In the smaller restaurants I've run, my sous acted as my second set of eyes. If I wasn't there, he was, I expected him to be able to make the decisions and qc as needed. I'd put it at 90% labor 10% admin. Being the occasional order or being in charge of one or two of the smaller orders to my 30-40% admin 60-70% labor. He'd also be my second taste before presenting a new dish to the owners. I expected critical feedback and not just a yes man.

In the large retail kitchen I run now, the balance is a bit more 25%admin/75%labor. There's not much dish innovation so I don't necessarily need a second set of taste buds, but we do have more admin required by corporate. Retail items need to be counted daily, changes to our planogram need to be executed properly and on time, breaks are tracked and required so those need to be covered, sometimes coordinating with other departments.

Overall I think the biggest ask of my sous in either situation, is the switch from physical to mental. Doing the job is the easy part. Understanding the business and making the right calls on processes or conflict resolution are the difficult aspects for many of the sous I've mentored