If you are talking about electron flow through a metal, like copper, the electrons are very loosely bound in their atoms. In fact, the electrons are so loosely bound, for the most part, its impossible to say which electron goes with which atom. You wind up with a "sea of electrons" that are pretty much free to just wonder around the conductor.
(As is that weren't enough, I think the current consensus is that an electron is a "probability wave". It has a 50% probability of being here, and 25% of being there, and another 10% of being somewhere else. So, not only do you not know what atom the electron belongs to, the electron doesn't even have a definite position until someone tries to actually find or measure its position.)
Given that, the thermal motion of the electrons is much larger than their flow due to an electric field. So if you could actually track and watch all the electrons moving, you would see they are moving in all different directions. But overall, a few more electrons would be moving in the direction of current flow, and a few moving that direction might be going a little faster.
It's a very gradual "electron drift" in the direction of current flow that would be hard to see within the general chaos of other motion.
So my vote is for lots of skipping and collisions, and general chaos, and even lots of electrons moving in the wrong direction. If you could plot the positions of the electrons vs. time, the actual current flow would still not be obvious.
Steve