How are the importance of sutras determined? I assume that there variations of sects within buddhism that deem certain sutras  as more "correct" or being closer to the buddha's teaching. I personally see the Lotus sutra as the "true teaching", but I know that some other sects often see the Flower-garland sutra as being closer to the "true teaching".  Is there a system for determining such assertations, or is it more based on text evidence? I have little knowledge with buddhism outside of the sect I'm apart of, so I'm interested in how other parts of Buddhism work.
In the Indo-Tibetan traditions, questions such as "what are the sutras of definite meaning? in what way are they different from sutras of interpretative, provisional meaning? what makes them sutras of definite meaning?" arise when we investigate the meaning of emptiness. This is because, since the wisdom realizing emptiness is the direct antidote to ignorance, it abandons the obstructions to liberation. Therefore, ascertaining the meaning of emptiness is of utmost importance, and it is why one has to rely on sutras 'of definite meaning' in order to do such ascertainment.

Roughly, a sutra of definite meaning is "more correct" when it comes to ascertaining the meaning of emptiness, but not necessarily with respect to other topics such as the method-side.

Thus, most texts and textual genres that mainly teach emptiness explain what sutras of definite meaning are and why they are taken to be so. They do that to show that they rely on reliable sutras, i.e. sutras of definite meaning, as opposed to sutras of interpretative meaning.

Examples of texts teachings emptiness are: 


Candrakirti's Madhyamakavatara and commentaries to it,
Nagarjuna's Karika and commentaries to it,
Maitreya/Asanga's Abhisamayalankara and commentaries to it,
Texts on the Tathagata Essence such as Maitreya's mahayanottaratantra-ratnagotravibhanga,
Presentation of the Special Insight Lam Rim chapter such as Atisha's and so forth.


The introductions to the Kagyu &amp; Nyingma commentaries of Maitreya's Ornament are worth studying in that respect. It explains the three turnings of the wheel and what is definite. (Blue-covered thick books titled Gone Beyond, and Groundless Paths)

Although the Tibetan traditions really are **Indo-**Tibetan, various Buddhist schools did not elaborate on and expanded much on Indian commentaries such as the ones I listed above. For instance, Chan (and later on Zen, Thyen, Seon) does not particularly rely on Indian sources. This means that you will hardly find what Chan masters answer to your question in commentaries to those texts. However, there are aspects of early Madhyamika (and thus Nagarjuna) even in Chan.

Nagarjuna and Maitreya/Asanga are Indian sources that have been elaborated on a great deal by Tibetan Scholars, but also by other traditions such as Tiantai, Pure Land, etc.



The Prasangika-Madyhamika school of Tenets say:


Sutras of the Pali canon are provisional and are the first turning
Perfection of Wisdom Sutras are of definite meaning and are the second turning
Sutras of the third turning are usually of provisional meaning, except those which meaning accord with the Perfection of Wisdom Sutras, such as the Tathagatagarbha Sutra.
Prasangika posit that a sutra which main subject-matter is emptiness is of definite meaning. Sutras of the Pali canon that speak of emptiness are not of definite meaning because they do not teach the final view on emptiness, the lack of inherent existence. 


The condensed version of the Pefection of Wisdom sutras is the Heart Sutra.



Chan masters were initially called 'Lankavatara masters'. However, the Lankavatara Sutra was so difficult to understand that, later on, as Chan popularized and became less provincial, the Avatamasaka Sutra (Garland of Flowers Sutra) took over. Thomas Cleary made an amazing translation of this particular sutra, about than 1'600 pages. Furthermore, the introduction of the English translation of the Avatamsaka states that according to Chan:


The Avatamkasa was taught by Buddha in a pure Land, after he showed the aspect of achieving enlightenment and before he taught the sutras of the Pali canon. It is of definite meaning. 
Sutras of the Pali canon &amp; Perfection of Wisdom Sutras are the second turning of the wheel, and of interpretative, provisional meaning.
The Lankavatara Sutra, Tathagatagarbha sutra, etc. are the third turning and, like the first turning, of definite meaning.


The third turning of the wheel sutras explain the three natures. It is called 'the turning of correct differentiation (between what is and what is not truly existent)'. The condensed version of the Avatamsaka is the King of Prayers.

Pure Land Buddhism highly regards the following three sutras:


Infinite Life Sutra,
Amitabha Sutra,
Meditation Sutra.


However, I do not know whether they posit them as being 'of definite meaning', and which turning of the wheel they claim these sutras belong to. 

My answer is all in all very incomplete.