When comparing these two passages, the Sfas Emes notes that the two share the theme of menucha, or "rest". The Sfas Emes, when explaining the original Shabbos in Bereishis (Genesis), writes that in truth, rest is not simply a pause from physical activity, but the Hebrew word menucha is meant to express a complete cessation from anything. He says that when we follow the Torah and halacha (Jewish law), we allow our real (spiritual) selves to rest from the false physical desires that distract us from G-dliness. Therefore, rest in the realest sense means to distance ourselves from something.
From this understanding of the word rest (menucha), we can see that whenever something subjugates itself to the Divine will, thus distancing itself from physicality, it is in the realm of "resting". In commenting on the first Shabbos, Rashi explains that this was the time when rest was actually created. At this point everything that was to be created was reated, and it sat perfectly in the Will of G-d, thus creation rested.

With this understanding of rest and creation in mind, the Sfas Emes explains the first verse metaphorically, speaking to the purpose of our lives. In this world (the pre-Shabbos workweek), our task is to bring ourselves into the reality of living a life that is within the complete Emes (truth) of the Creator. The mention of the donkey and bull, therefore, are references to our current physical nature. It is our job, through struggle and pressing ourselves into the reality of our spiritual selves, that we bring these physical desires into compliance with our true essence. When we succeed in this, we fulfill the verse, and our own bull and donkey (physical nature) is allowed to rest, or distance itself from the sheker (falsity) of the world in which the Divine is hidden.