If a full balcony off of your room is important, I suggest staying at the Yacht Club, as about 99% of the YC rooms have full balconies. Many guests like to sit out with their morning cup of coffee or just take a break and relax, sitting on the balcony. Only about half of the rooms at the Beach Club have full balconies, with the other half only having Juliet (standing) balconies. You can request a full balcony at the Beach Club, but it's only a request and never guaranteed.
Both resorts recently refurbished their guest rooms. As part of the refurbishments, the YC rooms had carpet replaced with wood laminate flooring, and ceiling fans were removed. Those rooms also had many of the tub/shower combos replaced with walk-in showers. The height of the new beds is about 5"-6" higher than normal, making it a little difficult for shorter guests or guests with physical challenges to get into bed.
The Beach Club still has room carpet, ceiling fans, and mostly tub/shower set-up.
The walk to Epcot takes about 5 minutes from the BC and only a few minutes more from the YC. The Friendship boats, which can take you to Epcot, the Boardwalk, Swan/Dolphin and Hollywood Studios, are closer to the Yacht Club.
The recreation, shops, and restaurants are shared by both resorts.