You get to do both. The concept of "you" changes once there is a copy, see the Ship of Theseus [1]. Each post-you entity has a legitimate claim to being pre-you. The copy woke up that morning, ate your breakfeast, went to the uploading clinic, and went to sleep as a digital being. The copy has perfect continuity. The biological you on the other hand stayed biological and will die.
A gradual replacement doesn't change the fundamentals, the biological you has to die. The gradual replacement just makes for an unusual twilight, its mind commingled with an arising digital being.