Would Beowulf be considered a hero today? If not, what examples could be used to explain the difference in time periods?
What examples are there that shows how Beowulf's decisions then would not define a hero today?
This question is largely a matter of opinion. Some people will see him as a hero and others will see him as the problem of our modern world. In a words, opinions will run the gamut. Here are some reasons why people will see him as a hero. First, he is a great warrior. He defeats Grendel, Grendel's mother, and the dragon. Second, he is brave. He does not allow those beneath him to fight. He does it himself. In this sense, he is fearless and selfless. These are qualities that many people will admire.
On the other hand, some people might not see him as heroic at all, but a proponent of the problem of the world. They might argue that the problem of the world is conflict and fighting. Why does not Beowulf seek peaceful solutions? Why does he not give back the treasure that was taken from the dragon? Even if the dragon does not accept this gesture, peace should be sought.
Unfortunately the poem starts in media res (in the middle). So, we have little context. With more context, there might be more consensus. In the end, all people are different and their code of morality is different as well. We can confidently say that Beowulf will elicit an opinion. Some social theory should help a bit in understanding this.