I answer at this place because I cant do at the point of your so called "pain in the ass."
There is a difference in the grammatical structure of those sentences - though they seem to be equal according to your impression.
Ezek régi polcok. <=> Ezek a polcok régiek.
In the left sentence the adjective (old = régi) is used as an Attribut. So it is connected with the noun. (old shelf = régi polc)
In the right sentence the adjective is used as an adverb! It is connected to the verb. (That there is no verb to be seen in the Hungarian sentences is a special fact of the verb "van", which is used in the 3.persons only for the means of "it exists")
So you hopefully understand the difference between an attribut and an adverb.
And there is a grammatical difference in Hungarian using them. An attribut is always used in singular form allthough the connected noun might be plural.
old shelf = régi polc ; old shelves = régi polcok
... so far the same in English.
But an adverb has always to get the pluralform, if the connected verb is in plural.
Ez régi polc. = This is an old shelf.
Ezek régi polcok. = These are old shelves.
Ez a polc régi. = This shelf is old.
Ezek a polcok régiek. = These shelves are old.
It may mean the same but it is not the same sentence. It is the translation of a different sentence. :)