I have left the dock area at about the same time as the boat. I got to Epcot bag check as the boat was unloading. It's pretty close to even timewise.
But, going to DHS is a whole different story....my friend and I just missed boarding the boat at Intl Gateway to DHS....the pilots laughed at us and told us they would beat us to DHS..told them that wasn't going to happen!! Yes, they got to BW about 30 seconds before we did, but they then had to go to YC/BC, then to S/D. We didn't see them again until we headed to bag check at DHS..they were just coming around the bend towards DHS. I would say we beat them by 5-8 mins.
The walk to Epcot's International Gateway from BW is about 8-10 mins. The walk to DHS is about 15-20...depending on where you leave BW from and your walking pace.