Qur'an and Adhkar:
When reciting the Qur'an out of the prayer, it is is more favorably in Islam to read it with Tarteel which you wouldn't be able to do in whispering, and it is better to be done in a moderate voice.
Surat Al-Muzammel (73) — Verse 4, in Arabic (the exact wording):
وَرَتِّلِ الۡقُرۡاٰنَ تَرۡتِيۡلًا ؕ...
In English (in what it means):
and recite the Qur'an in (slow) measured [rhythmic tones / recitation].
But if there was something that prevented you in one way or another from that, then you go for whispering and murmuring/muttering.
The same is applied for the Adhkar (plural of dhikr) which can be said aloud in a normal or rhythmic way.
As what the verse 110 in Surat Al-Isra (17) means by:
قُلِ ادْعُوا اللَّهَ أَوِ ادْعُوا الرَّحْمَٰنَ ۖ أَيًّا مَا تَدْعُوا فَلَهُ الْأَسْمَاءُ الْحُسْنَىٰ ۚ وَلَا تَجْهَرْ بِصَلَاتِكَ وَلَا تُخَافِتْ بِهَا وَابْتَغِ بَيْنَ ذَٰلِكَ سَبِيلًا
When praying in congregation, you as the Imam shouldn't do the pray (which includes reciting the verses and doing the pillars of the prayer) too loudly to the extent that Polytheists would hear you so they may curse the Qur'an and Allah as they did in a similar situation with the Prophet (Peace Be Upon Him) Source in Arabic or any other people who may get disturbed or are non-Mahrams for women, and don't whisper it so that the people around you (your partners in the prayer and the people who are listening to you) wouldn't hear it so that they miss the benefits of it, but choose in between (moderate voice).
This also applies for those who pray alone (not in a group) in the Jaher prayers (first and second Rak'aa in Fajer, Maghreb, and Ishaa), which is indeed Sunna. For the rest of the prayers and Rak'aat, they should be done silently (murmuring or with your mouth completely closed). This is valid for both men and women. Source in English