Before I got my EGC, I was running my Ric with flats into the El Oso with the gain set low and the tone set to have a decent amount of unaffected low end. It did great getting me some low gain grit and added sustain. You can hear what I'm talking about in this video pretty well:
Your comparison between the BB and GS is pretty accurate. I feel like the GS is a little more swiss army knife, whereas the BB tone is a little more baked in. They come pretty close to the same tonal space. Not many people say they like one but not the other. The GS is more readily available, so if you can't get your hands on a BB, the GS is a great option and I'd say they're probably neck and neck as far as muffs go and the "winner" is going to come down to personal preference. I don't think you can lose with either.
No experience with the other pedals, sorry! Somehow I got lucky and the Bluebeard was the first muff I purchased early into my bass career, and I've never felt the need to look elsewhere