On the second day of Pesach an offering of barley flour is brought and is baked unleavened. On Shavuos the offering is made of wheat and is baked leavened. Wheat is generally provided as human food, barley is generally used as animal food (Talmud Sota 14A). Pesach marks the time we were given liberty from slavery and emerged onward with great material wealth. Shavuos is the time of our receiving the Torah at Sinai and continued onward with great spiritual wealth.
Unleavened bread is flat, hard and unembellished. Leavened bread is soft, high and more tasty. We have within us two diverse instincts - the animal instinct and the G-dly instinct. (Tanya Chapter 1). We must pursue both directions. - Six days shall you work and do all your labor (Exodus 20:9) - To love Hashem to walk in His ways, to observe his commandments, His decrees and His ordinances (Deut. 30:16)
On Pesach, which marks material liberty, the offering is of unleavened barely bread. Material pursuit should be flat, of incidental importance and with a small amount of joy and enthusiasm. On Shavuos, the offering is of leavened wheat bread. Regarding the pursuit of the spiritual, it should be of prime importance and gone after with full joy and enthusiasm.
At the creation of Adam and Chavah, Hashem told them: Fill the earth and subdue it, and rule over the fish of the sea, the birds of the sky and every living thing that moves on the earth (Genesis 1:28). The human should rule over the animal. So should our G-dly instinct have dominion over our animal instinct. The fulfillment of our freedom on Pesach was fulfilled by the revelation of the Torah at Sinai on Shavuos.