Are we just animals?

²⁶Then God said, "Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth."
Genesis 1:26


What is man's place in nature? How is he different from the animals?
Out of context, this verse has also been used to justify "progress" involving exploitation and destruction of the environment. 
What is it actually about?
It is interesting to read some of Karl Barth's exegesis, which not surprisingly is rather Christological,

... man stands in royal superiority over the animal. No technical proof is given of this superiority, either by reference to man's form or by reference to his rationality as the instrument of his sovereignty. Indeed, no such proof can be given if we are to be loyal to the spirit of the passage. Of course the asserted sovereignty has its basis, but this is to be sought only in the divine likeness of man, and therefore in the creation of man as male and female to the exclusion of all other differentiations, and therefore in the unity and uniqueness of the human race. ....

Adam and Eve in the Garden of Eden, by Peter Wenzel


...But the basis which emerges when this fact is joined with the words about man's divine likeness is not a technical basis. By reason of the fact that man is created in and after the image of God, and therefore in this uniqueness, no means are put at his disposal for the exercise of this lordship over the animals. What is given to him-and it is to this that the passage refers -is the divine destiny and promise of this lordship. .... For all his similarities and links with animals, he is not to be one animal with others, but is to have them all under himself-in correspondence with God's relationship to all creatures. He and he alone, male and female, is to be the one "animal" to whom God will reveal and entrust His own honour within creation, with whom, in the course of a special history which will not be that of any beast, He will make common cause, and from whose activity He will expect a definite recognition of Himself, the praise of His might and of His right. Obviously this lordship, this distinction, cannot give man a technical superiority over the beast. It rests exclusively on the divine destiny and promise of his divine likeness. It is the immediate consequence of this, and must not be separated from it. Only in this way is it the answer to the question of Ps. 8⁴: "What is man, that thou art mindful of him? and the son of man, that thou visitest him?" Only in this way does the answer which follows ( v. 6) have meaning: "Thou madest him to have dominion over the works of thy hands; thou hast put all things under his feet." Where is the fulfilment of this destiny and promise? ... [The Old Testament] tells us (in the story of the fall in Gen. 3¹) how in antithesis to the destiny and promise given to him man was deceived by the most cunning of the creatures over which he was to have dominion, and yet how in spite of this the destiny and promise ( Gen. 3¹⁴) were again renewed and preserved. It thus recounts the history of the covenant between God and man as it was fashioned in God's relationship with Israel. In the history of this covenant it becomes true that man was created, not to be the lord of creation, but to be a lord in creation and in token of this to be lord over the beasts. And the New Testament (Heb. 2^5f.) has given this answer a final and true elucidation by referring the whole of Ps. 8 directly to the man Jesus who, for the suffering of death, was crowned with glory and honour. A thoughtful exposition of Gen. 1^26f. will certainly have to move along the line which leads to this point. The biblical creation saga had no occasion to speak of any other lordship of man over animals than the one actualised along this line.

Karl Barth, Church Dogmatics 3.1, p. 206.