Vedas are not only just some chants or some type of books, they are the fundamental building blocks of this universe itself. Every part of universe is composed of some vibrating Veda mantras. The particles contain abundance of RigVeda (Ayam Lokoh RigVeda), the space consists of abundance of YajurVeda (Antarikshyam vai YajurVeda), the bright particles/light contain abundance of SamaVeda
Lord in Bhagvad Gita tells he is SamaVeda among the Vedas, in the Vibhuti chapter where all the things told are such which shows shining nature of all. Now, we have to find how SamaVeda is shining than other Vedas. For this we have to think of what are those places which contains abundance of Saman? For this we have to look upon pramanas of Rishis from Vedas.
Samans are very sukshma and we can't observe them directly with our eyes. But we can consider those particles which contain abundance of Saman as Saman themselves for understanding. And we get that the most appropriate representative of Saman is light. This is made clear in Shatapatha Brahmana:
The rays of light are Samans. (Shatapatha Brahmana 10.5.1.5)
From above verse we can have faint understanding of Samans. We can consider them as rays of light. Due to this everything which has brightness in this world contains Samans:
सर्वं तेज साम रुप्यम्
Whatever is brightness (Teja) in this world is all the form of Saman. (Taittariya Brahmana 220.127.116.11)
The above quotation is itself sufficient to prove why Lord Krishna says he is SamaVeda among Vedas it's because whatever bright (luminous) things/particles exist in this universe they all are formed from Saman. Saman vibrations (Rashmis) condense themselves and form light and other Teja form. Taittariya Samhita also confirms the above statement:
देवलोको वै साम
DevaLokas (Shining bodies) are Samans (Taittariya Samhita 18.104.22.168)
For the planetary bodies which are not shining (or do not emit light) we can use the term PrithiviLoka, for the lokas/bodies which are bright in themselves we can use the term DevaLoka (Div = To shine). Thus shining bodies like stars contain abundance of Sama Rashmis. In the spritual sense too we can understand the realm of Gods is composed of Samans.
The same thing is cleared again in Tandya Brahamana:
साम वा असौ द्युलोक
Samans are the world of stars/ bright bodies. (Tandya Brahmana 4.3.5)
Brightness of bright particles is only possible because they feed upon Saman. Light is not possible by only resting on Rik rashmis and Yaju rashmis. This is made clear in Taittariya Samhita:
देवा वै नऋच् न यजुष्य आश्रयन्त ते सामन् एवाश्रयन्त।
Devas could neither live on Rik, nor on Yajus, on the Saman only they rest. (Taittariya Samhita 2.5.7)
Saman are like annas for the Devas. A particle can be bright (Deva) only by feeding Saman Rashmis:
साम देवानां अन्नं
Samans are the food for Devas (Tandya Brahmana 6.4.13)
And most importantly whatever interactions are taking place in this universe is only possible because of Saman.
अयज्ञो वा एष योऽसामा
Without Samans there is no Yajna (interactions). (Taittariya Samhita 2.5.8)
From above all quotations it is clear why Lord told that he is SamaVeda among Vedas. But this doesn't mean that SamaVeda is the only superior and other Vedas are of no use. Each Veda and each mantra of Veda and each syllable of mantra is very important. Just like light/Archi are formed mainly from Samans similarly, Space/ Antariksha is formed from Yajush and Prithivi tatva are mainly formed from Rik.