(Big Band = Squigly > Eliza > Beowulf)
That's probably how I would rank them too. I mean, I don't think Beowulf's story was bad at all, but I just felt the other ones did a slightly better job putting me in the characters' shoes. For Beowulf, it wasn't until around the Marie fight and afterwards that I felt a genuine connection with the guy. I don't think this was a fault of the writing though, but just an overall challenge in dealing with this type of character in this format.
I think what makes Beowulf's Story Mode more complicated than the others, from a narrative perspective, is that it's dealing with a mature character going through a legit image crisis. He's fighting between who he used to be, who he wants to be for the people, and who he wants to be for himself. As a result, Beowulf's personalities before and after the Story Mode are just as important, if not moreso, than his personality during the Story Mode itself. Squigly, Band, and Eliza have fewer identity issues like this, so we can get a clearer picture of who they are within the brevity of their Story Modes.
As a comparison, I think Beowulf's Story Mode is similar to something like Darth Vader's fight with Luke on Cloud City. It's a series of climactic moments, where we see a lot of important character traits in a short span of time, but we still lack some context of how these events truly affect the characters in the long run. Likewise, I think Beowulf's story does a good job giving us slices of his character, and some climactic points, but it still leaves me wanting to know more. I can see where the character arc curves, but not the whole arc.
It's just one of those things that makes me so eager to see these characters revisited somehow in other media. I think a short graphic novel focused on Beowulf could go to some interesting places!