Is there an actual difference in meaning or nuance between 私達の世話をする and 私達を世話する?


I have seen this pattern where を is replaced by の in many sentences that use a
する verb. I got used to this construction by exposure and it has started to
look less clunky and more natural to me, but I would like to know:

1）Is there is an actual difference in meaning, or at least in nuance, between
both patterns?

2) Are both options valid in any situation or should I pick only one of them
in any particular case?

I naturally would go with:

「姉が私たちを世話してくれた。」

as I understand the structure of the sentence as:

（私たち）を （世話する）（to take care of us）

However, I see the following pattern quite frequently:

（私たちの世話）を （する）(to do the take caring of us)

Now, don't get me wrong, I would never translate this into “to do the take
caring of us” but I would translate it as “to take care of us as” well, but
hopefully you can see my point this way.

I think that what made it mind blowing for me was that coupling the suru verb
as a noun to the previous word (the object, in my example 私たち) somehow
“detaches” the verb from the actual subject (姉), but at the end of the day
it's just a matter of getting used to it.

Finally, I suspect this is somehow related to the が/の substitution discussed
here:

[How does the の work in
「日本人の知らない日本語」?](https://japanese.stackexchange.com/questions/12825/how-does-
the-%E3%81%AE-work-
in-%E6%97%A5%E6%9C%AC%E4%BA%BA%E3%81%AE%E7%9F%A5%E3%82%89%E3%81%AA%E3%81%84%E6%97%A5%E6%9C%AC%E8%AA%9E)

Thank you very much!

