If Beowulf does his best to lead and support his thanes - by, say, spending the experience points he earns on upgrading their weapons rather than his own abilities - they'll gradually become much more effective, self-sufficient fighters, and you'll be able to command more of them at once. They might even sing better songs during the monster-luring minigames. On the other hand, if you run around being brutal and ignoring your thanes, they'll become weaker.
The ultimate example of this attitude is Beowulf's "carnal rage" power, which sends him into a blind, berserker rage that makes him super-powerful, able to rip enemies apart with his bare hands, but it also makes it impossible to distinguish between friend or foe. You run a high risk of snapping a few thanes in half if you activate this, and if you do, they'll come back to haunt Beowulf later on.
Reliant on his thanes or no, Beowulf is pretty formidable on his own. Big and beefy, he doesn't really need a weapon to kick ass (in the poem, after all, he kills Grendel by tearing off the hulking creature's arm), but he can pick up rocks, bones and even enemies to use as handy clubs. If you'd like something more traditional but don't want to dirty Beowulf's sword, you can even wrest away an enemy's blade and use it against him. He's also got a full complement of gruesome finishing moves, which will likely change depending on which path you're following.