The difference isn't necessarily formality. As a native English speaker, seeing the sentences with no context, my knee-jerk interpretation is this:
"Are the grapes his or ours?" = "Thers is a single set of grapes in question, and I don't know whether they belong to him or to us."
"His grapes or ours?" = "Which grapes do you mean? The grapes that belong to him or the entirely different grapes that belong to us?"
Granted, with the right context, it could mean the same thing as "Are the grapes his or ours?", especially informally, but I think thevpost you're responding to is asking about the distinction I just laid out.
And even if they weren't, I am :)