I've stayed at both and I prefer the Poly (but would stay at the Beach Club again!) Here is why:
The monorail - at the Poly, I can take the monorail directly to MK or walk to the TTC to take the monorail to Epcot. Since these are my two favorite resorts, this works well for me.
The pool - My kids are still small enough that I want my eye on them in the pool (even though they are good swimmers). At the main pool, I can sit in one spot and see them anywhere in the pool. And I get a view of Cindy's castle to boot! At the Beach Club, I had to constantly move with the kids to keep an eye on them and I disliked that the slide entrance was past the main walk. As my kids get older, I'll be fine with this though.
The food - BC has a very limited menu in their 'quick service' area where Poly has the yummy Capn Cooks where I can get a Mickey waffle or grown up grilled cheese or a dole whip! I also prefer all the restaurants at the Poly to the ones at BC or YC or even on the Boardwalk.
The rooms - I do not like the regular room layouts at the BC where the sink is outside the toilet/shower area. I do not want to keep my family up or have them keep me up as we all brush our teeth, dry our hair, etc. I like the Poly where the sink is in the bathroom and the noise can be contained behind a closed door.
I think if you are going to go mostly to Epcot and HS though, BC is a better choice. But if you are mostly going to MK and Epcot, Poly is a great choice.