I understand that は and が can be very different in meaning & emotion, and some structures require one of them. However, are there some cases where I can use either of them but the sentence remains (almost) the same in meaning & emotion?
(That is to say, given the same context, a native speaker would choose to use either of them to express the same idea.)
Actually, yes.
In negative sentences は often replaces が or を. E.g.
本は読まない (hon wa yomanai) I don't read books.
彼は好きじゃない (kare wa suki jya nai) I don't love/like him.
In these sentences, it would also be grammatically correct to use を and が respectfully, but many Japanese find は to be more natural. The rule of thumb is that there needs to be at least one は in negative sentences. If you add 私は at the beginning of the sentences above, the need for は is satisfied, therefore speakers are less compelled to use は instead of が or を. In negative sentences it may even follow particles like に or で to satisfy this condition.
英語では話したくないです. (eigo de wa hanashitakunai desu) I don't want to talk in English.
I hope this helps.
