Learn English – “based in” vs “based out of ”

The first is a little more casual than the second, and possibly found more in American English than in British English.

The difference is very subtle and not at all important. Both sound natural.

If you want to slide a cigarette paper between them, of uses the metaphor of constituent parts, and in the metaphor of container of objects.

So you could distinguish them by how much you wish to imply that the expression/clause has fixed, organised, and inevitable internal structure.

For example, the "subject of the sentence": there is one of them, and it's exceptional for it not to be there, an inherent part of the structure of a sentence: it is a formal part.

But "the adjectives in the sentence", as they can be scattered to various points in a sentence of any complexity: they are contained within it.

There's a vast plain of middle ground (where your example seems to lie) where it seems to make very little difference.