When to use 座る vs 坐る

Question

As I'm starting to explore more kanji, I've come across these two ways of writing すわる (to sit): 座る and 坐る.

I would like to know when to use one over the other. Are there nuances that would make one very inappropriate to use in a special setting? Is one being used for sitting with a roof over one's head (a house) vs under open sky (on a bench in a park)?

Answer 1

To built up a bit on my comment (坐 is old school 座. Now, you might only see the former in books and museums (it's quite common to see 坐像{ざぞう}). May be there are nuances but I never heard of.) 語源-allguide has an entry on 座る.

【意味】 座るとは、膝を折り曲げて腰を下ろす。ある地位や役に就く。

【座るの語源・由来】
座るは、落ち着いて動かないことを表す「据わる（すわる）」と同源。
「居ても立ってもいられない」と言うように、古く、「立つ」の対義語は「居る」であった。 平安時代末頃から、「居る」が「存在する」といった意味で多く用いられるようになったことから、他動詞「すう（据う）」が自動詞化した「すわる」が、「立つ」の対義語として用いられるようになった。
漢字の「坐」は「人＋人＋土」で、地面に尻をつけることを示している。
「座」の漢字は、「广（いえ）＋坐」で、家の中で人が座る場所のことである。
「坐」が動詞、「座」が名詞として用いられたが、常用漢字では「座」に統一された。

Translation:

座る means bend your knees and seat your rear. Or, be employed at a position.

[Etymology of 座る]
座る shares its etymology with 据｛す｝わる and means being calm without moving.
As seen in 「居｛い｝ても立ってもいられない」(boils at the core but can't afford not keeping calm), the antonym of 立つ was 居る.
Since, by the end of the Heian era, 居る became used a lot in the meaning of to exist the transitive verb 据｛す｝う turned into the intransitive verb 据｛す｝わる and (すわる) started to be used as the antonym of 立つ.
The kanji 坐 is made of 人＋人＋土 and means to seat one's rear on the ground (as you have guessed in your question).
The kanji 座 is made of 广（いえ）＋坐 and refers to a place where one would seat in a house. 坐 was used as a verb, whereas 座 was used as a noun. But this 坐 is not a 常用漢字, 座 is now used for both.

Answer 2

坐る is very rarely used. I have seen it little.

As far as I searched, 坐る was a Kanji for a verb, and 座 was a Kanji for a noun that means a place to sit in early Showa era.
Though the government enacted the following rules in Showa 31th(1956). http://kokugo.bunka.go.jp/kokugo_nihongo/joho/kakuki/03/pdf/doon.pdf
× 坐→座

It seems that they were unified into one Kanji by this rules. That is to say, 坐 is old Kanji.