My kids are older. The first time we took them they were pre-teens, the second time they were teens. We've always managed to do Epcot on one day. We are mid day break people, but we don't take a mid day break on our Epcot day. We rope drop FW, ride everything, have lunch at Sunshine Seasons then head to WS for the afternoon and evening. If I had little ones or wanted a mid day break, I'd probably spend 1.5 days in Epcot. I also really like the idea of rope dropping a different park each morning, taking a break and hopping to Epcot for dinner a few evenings.
WS can take you a long time to tour or a very short time, depending on what you enjoy doing. When my kids were pre-teens they enjoyed the Kidcot stops. As teens they enjoyed the demonstrations, street shows, snacking and having dinner at a nice TS restaurant. We are not big shoppers so the stores really didn't wow us. The last hour we end up find spot on the grass to rest and wait for Illuminations.
My SIL took her younger kids (3, 7, 8). They did not enjoy Epcot at all and plan to skip it next time. One day was more than enough for them. To each his own.