As others have said, Epcot and DHS are both walkable from the BC. It's about 1.4 miles to DHS (about the same whether you go via the Yacht Club or the Boardwalk) and about 0.25 miles to Epcot (may be closer depending on where are you in the resort).
The boat ride takes about 25 minutes from Epcot to DHS, once underway. It goes from Epcot -> BW/BWV -> YC/BC -> S/D -> DHS -> S/D -> YC/BC -> BW/BWV -> Epcot. The boat runs until one hour after park closing, so if Epcot is still open but DHS has been closed for a hour, the boats forgo the DHS leg of the route. One of the biggest drawbacks to the boat is that the dock is at the Yacht Club. So if you're staying at the BC, you'll have to walk over to the YC dock.
Whether walking is faster or slower depends on how fast you walk and how long you have to wait for the boat. My family uses the boat because there is already a lot of walking to do at WDW and we'd rather save our feet for inside the park. Either way, it's pretty easy to get to DHS and Epcot from the BC.