Neither. Itihasas & Puranas (histories) are not part of Shrutis or Smritis. Definitely not smritis. It is in its own category - Itihasa Purana - they are sometimes also called the Fifth Veda. This is given in the Vedas themselves:
"itihāsapurāṇaṃ pañcamaṃ (fifth) vedānāṃ" - Chandogya Upanishad (7.1.2)
"As clouds of smoke proceed by themselves out of a lighted fire kindled with damp fuel, thus, verily, O Maitreyî, has been breathed forth from this great Being what we have as Rig-veda, Yagur-veda, Sama-veda, Atharvâṅgirasas, Itihâsa (legends), Purâna (cosmogonies), ... From him alone all these were breathed forth." Bṛhad-āraṇyaka Upaniṣad 2.4.10.
"All the Vedas are manifested along with the kalpas, rahasyas, Brahmanas, Upanishads, Itihas, anvakhyatas and the puranas." - Gopatha Brahmana purva 2:10.
"The Itihasas and Puranas are Vedas." (yad brahmananitihasa-puranani) - Taittiriya Aranyaka (2.9)
Their divine origin is also mentioned in the mantra portion of Vedas:
Atharva Veda 11.7.24: “The Rg, Sama, Yajur and Atharva became manifest from the Lord, along with the Puranas and all the Devas residing in the heavens.”
Atharva Veda 15.6.10–12: “He approached the brhati meter, and thus the Itihasas, Puranas, Gathas and Narasamsis became favorable to him. One who knows this verily becomes the beloved abode of the Itihasas, Puranas, Gathas and Narasamsis.”
So they are neither Shruti nor Smriti, but they are about equal to Shruti.
There are many characters in Mahabharata and their words are very contradicting at times. So you cannot say just because something is in MBH it is authoritative. There are lots of bad people speaking and their word is not authoritative. So coming to Bhagavad Gita it is dependent on whether you are Vaishnav, Smart, Shaiv or Shakt.
- If you are first two you will consider it pretty authoritative, just like Shruti for many Vaishnav
- If you follow Shiv-Shakti then Vaishnav Itihasa, word of Krishna has little importance and is not authoritative. It is words of Shiv-Shakti in MBH that are important and like the Shruti.
- According to some Shaktas, Krishna was avatar of Kali so it becomes authoritative, close to Shruti