Is there any significance to the BwB using hanging as their preferred method of execution as opposed to beheading?

I think there’s a couple different reasons: 

1. Hanging is a more plebian way to be executed (historically, beheading was something of a perogative of the nobility) so it fits the BwB’s politics.
2. Hanging is much easier to carry out, whereas beheading requires both strength and precision; 
3. Unless you have a long enough drop, hanging is a slow, drawn-out way of executing someone, so it’s way more painful than cutting someone’s head off.