I run in both. I actually use the Adios for a trainer, and race in the Boston, even though the Boston is heavier.
I'm a mid-foot striker, and I find that in the Adios the Boost is mainly in the heel (the forefoot feels paper thin), while it's in the entire sole of the Boston. Because of that, I feel that I get a lot of bounce from the Boston that I don't from the Adios, and run faster.
At the same time, because the Boston is so soft, I can't wear it for a daily trainer - my ankles get tender. Similarly, the Boston doesn't work for me on a track - soft track+soft shoe is a problem.
(so yes, I use lighter shoes for my daily training, and then put on the heavier shoes for races - but it works for me).
Both are good shoes. Adios 2 was also pretty narrow in the forefoot (at least as compared to the Adios 1); the Boston is a bit better there.
FWIW, I've also found that any shoe with Boost in it seems to last forever, so don't let the high price tag scare you. The Adidas Boost line also seems to have very good traction on slick/icy surfaces.