So your brakes work fine? Your stopping distance isn't affected? Kind of a mushy feeling under your foot, with no idea what's really happening at the wheels? Sounds like you're driving a Ford. I'd say it's your booster but I'd expect the opposite effect, unless your foot is going to the floor when you start it with your foot on the brake. Just did a master cylinder and booster on a Honda, MC was leaking into the booster & shit was all rusty so we did them both instead of just the MC. The pedal was gradually going down at lights, felt a bit light on pressure going down but the brakes worked great. The pedal pumped up hard with the car off but got really soft as soon as the car started. Your problem is in either the MC or booster. I'm leaning towards your booster as that MC had been leaking VERY slowly for several years and this came on pretty fast.
I know it's a different car, but the parts are the same fundamentally.