"Grandfathers are people."

I just did a quick check by looking at word frequency in two recent Esperanto publications. "Homoj" is more common. It's important to consider the intended meaning, however. It's like asking which is more common in English: human (being) or person?

If you consider the semantic space occupied by "human (being)" and "person", a similar semantic space is occupied by "homo" and "persono". The difference is that "homo" (compared to "human") is a little broader in meaning and use and will be seen in many contexts where we say "person" in English - such as the one in the OP.

The core meaning of "homo" however, is human being - so if you mean human being, you HAVE TO say "homo". If you want to emphasis personhood, that is, the rights of the individual or the division of God into three persons... you have to say "persono."

Jes, mi auxdas "homoj" pleofte.

I disagree. At the very least, I think it's the wrong question. They mean different things.

Is the difference similar to "people" versus "persons" in English? (So, for example, although it is linguistically acceptable to say, "Grandfathers are persons", it would come across as awkward or legal-ish.)

no accusatives after 'estas'

No, it wouldn’t, esti (“to be”) is not a transitive verb, but a linking verb. It cannot take a direct object, hence no accusative here. It links two parts of the same rank which are both in the nominative.

In connection with a verb the accusative is used only for direct objects. These verbs are called transitive. (Mi vidas lin. – I see him. versus Min vidas li. – He sees me.).

There are intransitive verbs which do not take an direct object. (Mi dormis. – I slept.)

And there are linking verbs as explained. (Mi iĝos kuracisto. – I will become a doctor.)

Because in English only with some pronouns (I/me, we/us, she/her, he/him, they/them) the accusative is marked, it is difficult to see it in English examples. And because of the lazy use (Is it me? instead of Is it I?).

Did you write "Avojn estas homoj(n)"? Avoj is subject, it has to be nominative, as homoj because "homoj" = "avoj", none of them is an object.

Esti (to bo) is a linking verb. It links to things on the same level, neither is an object. So there is no accusative.

Did you just say "avoj?"