Hi Kim,
You are considering two great resorts. My family has stayed in one-bedroom villas at both Disney's Beach Club Villas and Disney's Boardwalk Villas with our young daughter. The one-bedroom units in each are very similar, so your decision will likely be based on the other amenities at each resort.
Location-wise, these resorts are very close together and have easy walking access to the same places. From either, you can walk to the International Gateway entrance of Epcot, though the Beach Club walk is a little shorter. You can also take a boat from either resort to Epcot. Both resorts provide bus transportation to Magic Kingdom and Animal Kingdom. Both resorts border Crescent Lake and are within five to ten minutes of walking distance of each other.
Your decision will likely me made by your feelings about the theme of each resort.
Disney's Boardwalk Villas is themed to turn-of-the-century Atlantic City. There is a lot of hustle and bustle. At night, live performers take to the Boardwalk. Luna Park Pool at the Boardwalk includes the Keister Coaster, a long water slide which culminates in shooting out of a clown's mouth. Dining options include Flying Fish Cafe for upscale dining, Big River Grille and Brewing Works for burgers and beer, and the Boardwalk Bakery for a quick sweet bite.
At
Disney's Beach Club Villas, the atmosphere is a little more relaxed. It is themed as a New England-style resort. Many people love Beach Club for Stormalong Bay, a large pool, portions of which are sand-bottomed. This pool includes a long pirate ship slide. Dining at the Beach Club includes Beaches and Cream, a soda shop perfect for casual burgers and ice cream.
This is a tough decision, but you will win either way. Have a wonderful trip.