The Lubavitcher Rebbe explains (Likuttey Sichos vol. 33 pg. 18, adapted in English here):
The Gemora (Chagiga 13b) explains the difference between the Merkava of Yishayahu and that of Yechezkel:
כל שראה יחזקאל ראה ישעיה למה יחזקאל דומה לבן כפר שראה את המלך ולמה ישעיה דומה לבן כרך שראה את המלך
All that Yechezkel saw Yeshayahu saw. What does Yechezkel resemble? A villager who saw the king. And what does Yeshayahu resemble? A townsman who saw the king. (Rashi: The sight of the king is a novelty to the villager, and he is naturally inclined to give his impressions at length. However, the king is a familiar sight to the townsman and he does not need to elaborate in his descriptions).
Although both prophets merited visions of the Merkava, Yeshayahu's was more clear and direct. Yechekziel however, being an "outsider", focused on the “entourage” (the animal-like images etc.), whereas Yeshayahu being more comfortable with his exposure to Divinity was able to look through the "entourage" and focus on G-d Himself.
It would thus seem more appropriate to read about the vision of Yeshayahu on Shavuos, which describes a superior revelation of G-dliness. However, the Lubavitcher Rebbe explains, when we understand the purpose of Matan Torah we can appreciate how it is the vision of Yechezkiel which is more fitting with the theme of the Giving of the Torah. The Giving of the Torah was not an isolated event; its purpose was to enable us to sanctify and bring spirituality into this physical world. This is only possible because the physical world in all its details is a reflection of the spiritual worlds from which it was formed. Sanctifying this world is the process of identifying and re-associating each physical entity with its spiritual counterpart.
This is the theme expressed in Yechezkiel's vision. Just as Yechezkiel saw imagery of the heavenly "entourage" through which he was able to discern its Divine source, likewise, we should train ourselves to see through the veil of physicality and appreciate how every element of this world is merely the external face of a higher spiritual reality.