I didn't get into K-pop until early 2014, so I'm honestly not too sure about just how big/popular Boa was in her prime. Obviously I know how much Boa was (and is) loved by a lot of older K-pop fans. I also know how Boa has influenced some of the idols today.
I only really know about and feel Taeyeon's influence, when comparing to Boa. The reason being is that whenever I see someone asking about who the Queen of K-pop is, they name either Taeyeon or IU (between the two, IU is probably named more though). And this is a recurring theme since 2014. A lot of girl idols that debut also talk about their influence being SNSD, with some even mentioning Taeyeon. This is also quite a common theme since I got into K-pop.
Given where K-pop is at right now, and how active and popular Taeyeon still is, along side SNSD still being one of the most popular GG's, I'd say Taeyeon has surpassed Boa. In terms of influence anyway, so I guess Taeyeon is more of a Queen lol.
I won't get into who is more of a queen between Taeyeon and IU though, as that's impossible to say.