I raised a similar question about the tense of verbs modifying nouns, which I think also applies here - the only difference is that the nominaliser の is being modified instead of a regular noun. Other users can give their assessment of the answer which I got from a teacher of Japanese.
Short answer:
The plain and "past"/"perfect" stative verbs are more objective and are therefore more likely to be used in the media. The present progressive (〜ているの)is more subjective and therefore more likely to be used by the person performing the act.
Full answer (including non-stative verbs):
I wanted to know the difference between expressions where the verb modifying a noun is in dictionary form, past-perfect form or ている form.
Expression prompting my question: 会話能力を持った初の人間型ロボットキロボ
(ie: 持ったN vs 持つN&持っているN)
The answer was as follows:
(I can translate if there is enough demand):
こちらは状態を表す表現なのでどちらでもいいです。持つ、持ったのほうが、客観的(書き言葉的)に聞こえます。
アクションを表す動詞の時は、現在・過去の意味が入ってしまうため辞書形・ているを使うときと過去を使うときで意味が違います。
状態動詞例)
山の上に立つ家・立っている家・立った家 (全てOK)
アクション動詞例)
山に登る人(未来or 繰り返しのアクション)・
山に登っている人(現在進行or繰り返しのアクション)・
山に登った人(登ったことがあるか、登り終わった人たち)
Regarding the difference between stative verb forms 山の上に立つ家・立っている家・立った家 (or in your case 住んでいるの vs 住むの):
The plain and "past"/"perfect" verbs are more objective and are therefore more likely to be used in the media. The present progressive (〜ているの)is more subjective and therefore more likely to be used by the person performing the act.