As an "Epic Hero," Beowulf would be a modern day warrior. Due to the sheer amount of blood and gore in Beowulf, I can't imagine that Beowulf would simply fight "injustice," but would consider the actual bloody conquest of the enemy to be the way to win. Precisely because Beowulf is an epic hero, if he existed in the modern world, he would have the characteristics of the epic hero in literature. Therefore, the modern day Beowulf would have at least some of the following characteristics: larger than life and almost divine, quest against a horrid adversary, intelligent especially on the legends of his people, he would be strong, and he would be brave. You can see all of these qualities hidden in the paragraphs below. In regards to your question, the modern Beowulf would both prosper and suffer, his worldview would fit in America (but possibly not in a global community), and he would most definitely be a military warrior (or vigilante).
He would prosper because he would be a role model and celebrity, fighting for what is good in the world. He would have an enemy, a SINGLE enemy. His own Grendel.
Remember your fame and be valiant; keep watch for the foe! No desire of yours will be unfulfilled if you come through the battle boldly with your life
In this regard, I think of the modern Beowulf specifically as the anonymous soldier who was able to find and kill Osama Bin Laden. The difference is that the soldier of today is unnamed. Why? The honor needs to go to the United States Military and not to the one soldier. It is a fundamental difference in culture for that to be the case.
However, a modern Beowulf would also suffer because he would truly be killing the enemy. That type of (often "military") hero always has enemies in pacifism. Much of the world (especially the intelligent European, Western world) believes in pacifism. Negotiation is ALWAYS admired over violence. Even though many would see the adversary as a "terrorist," and therefore not someone who could be talked to, some would always try for peaceful negotiation. That being said, an unnamed soldier DID find and kill Osama Bin Laden in his HOME, no less. This is VERY similar to Grendel! Most Americans celebrated, but most everyone I know had a bit of worry about that celebration in that we were celebrating the death of a human being (and not the death of an actual, mythical monster like Grendel). As a result, the military was criticized. This criticism might be another reason the soldier remains anonymous: he needs to be protected. Ironically, he needs to be protected from irate pacifists. Note Beowulf's own words:
We men are the monsters now. The time of heroes is dead, Wiglaf - the Christ God has killed it, leaving humankind with nothing but weeping martyrs, fear, and shame.
His worldview would be limited to his particular culture; therefore, I'm not so sure Beowulf would fit into a global society, but he would certainly fit into AMERICAN society and the American military. America is often criticized for being "unilateral" these days, for thinking of only our own interests. As a result, I think his lust for blood of the enemy would be looked down upon in places like Europe. This would especially be true of the soldier who killed Osama Bin Laden. He was praised in America, just like Wiglaf praised Beowulf here:
He was the bravest of us. He was the prince of all warriors. His name will live forever. ... You are Beowulf. Beowulf the mighty, the hero! The slayer and destroyer of demons! Now let us kill this flying devil where it sleeps and get on with our bloody lives!
We were seething from the attacks of 9/11 and Bush proclaimed "dead or alive." Americans preferred dead. As a true epic hero, the soldier performed! Praised in America, protected elsewhere.
His role in society would not necessarily be as military leader, but as a soldier who leads from the front lines (perhaps in the American "special forces"). Military leaders these days have extensive experience in fighting, but they don't generally pick up a gun anymore, they are more funneled to management positions. Beowulf would never allow that: he wants to be part of the fight, always. This is certainly true of the soldier who killed Bin Laden. It wasn't Colin Powell who did so. It wasn't John McCain. It wasn't Oliver North. Nope. It was an unnamed soldier. Therefore, this is truly different than the Beowulf of old! Beowulf would want and even NEED the praise! Our soldier would have to be content with anonymous conquest and, as a result, anonymous joy.
In conclusion, amid the prospering and suffering and philosophy and military role, I'm not sure humanity is quite ready for a female Beowulf. I can certainly think of a few proposed (albeit imaginary) females that would work, such as Laura Croft. However, I just don't think someone like Hillary Clinton would fit the bill (even though she might end up being our Commander in Chief). I just can't imagine her hands all bloody with enemy gore. (SO many puns in that statement!) UNLESS, it is killing her husband after an incident with Monica. However, I wouldn't put it past our military to specifically have a woman in that combat role and, in that, what a shame that she is anonymous! If so, perhaps there will be a delay in proclaiming her. Maybe after she has passed on, ... or made a Major General.