この記事についてのご意見をお聞かせください。
Please tell me your opinion about this article.
新しい事業計画につき、これから御説明いたします。
Now I'd like to talk about the new project plan.
Not interchangeable in the first sentence due to the の after について.
But this would be fine:
新しい事業計画について、これから御説明いたします。
Now I'd like to talk about the new project plan.
- Also, 「につき」has an additional common usage
which isn't interchangeable with「について」:

Here it is the same as saying, 「工事中なので」or「工事中のため」
"Due to Construction" / "Because of Construction"
"Please Refrain from Parking"