They really are completely different things in my opinion. They share the common ground of being 2D fighters but the similarities end not too far from that. Of the many things I hate about SF, lacking character diversity and boring gameplay are the top two. It seems like every other character in SF is based on the same template as Ryu, with slight modifications being made but very few unique differences.
BB/GG are way more energetic in my opinion. There's lots more legwork involved in getting your character to do what you need it to do. BB/GG definitely have more focus on combos, sometimes very long ones, which I hear a lot of SF players detest. From my personal experience, SF feels very rigid and artificial in terms of movement/actions. For instance the way everyone just "forward steps" in SF whereas BB/GG most of the cast can run forward and stop whenever they want on a pixel-by-pixel basis. Some players like the restrictive feel to SF, because it emphasizes a sort of focus on pure fundamentals. A lot of the attacks in SF just feel like identical-length pokes to me. It's like the difference between a "fast" attack and a "slow" attack are only the recovery frames instead of the startup frames. I find BB/GGs movelists to be dramatically more dynamic than SF's.
Also, BB has squirrel girls and vampire lolis.