A big protein going through gel electrophoresis will be forced through the gel, it will drift a small way and will show on the top of the gel, while in size exclusion, the big protein is not forced to go through the pores and will elute first. Why is the protein forced through one medium and not through the other?
In the polyacrylamide gel, there is no way to avoid the narrow passages. The gel is made in situ by a chemical crosslinking step. In size exclusion, the solid phase is made of beads with diameter ranging from 50 to 200 µm diameter. The voids between these beads are connected and sufficient larger for the protein to go through.
Another difference between the two methods is the for SDS gel electrophoresis, the protein is denatured while for size exclusion, it is usually in the native state, so the shape and the flexibility is different, leading to different mobility.