のは～の方(ほう)だIt is...that..., It is...who..., ...is the one that..., ...is the one who...

Both structures single out and highlight something. That is, expressing '(A) is the one that (B)'. Adjective + の(は) is the simpler form, e.g. 新しいのはどっち？ ('Which one is new?') のはXの方だ expands on this to specify and contrast. A common use is in insistent apologies, e.g. いいえ、謝らないといけないのは僕のほうだ ('No, I'm the one who needs to apologize.')

のはXの方だ emphatically states what is true or relevant, often in contrast with something else, e.g. 勝ったのは彼の方だ ('He was the one who won.') わけではない, by contrast, qualifies or softens a statement, e.g. 彼が勝ったわけではない ('It's not that he won.') One affirms directly; the other downplays or denies.

Both structures single out and highlight something, but in different ways. のはXの方だ highlights contrast between options and is often used in apologies, e.g. 悪いのは僕の方だ ('I'm the one that's at fault.') こそ emphasizes exclusivity or importance, e.g. 私こそ謝るべきだ ('I, and no one else, should apologize.')