Nil to Negligible
Octagonal plates will be harder to position on the floor due to the plate edges. Its not uncommon for plates to rotate on a bar, so that as you return the plate to the ground it may shift slightly, and rotate the bar in a plane parellel to the floor.
This means you need to reposition your feet, but this is only a problem for floor exercises, such as deadlifts, cleans or snatches. Squats, overhead press and bench press are unlikely to be effected at all.
Presuming a difference in mass, the center of gravity and physics between the two plates is unlikely to be disernable.
Regarding height, again, there may be a slight difference in the radius of the octagon, depending on if the radius of a circular olympic plate is used for the distance to a corner, or the centre of the edge, or some point in between. But again, this difference is likely to be no more than an inch in height compared to a normal circular plate (that are also subject to differences between manufacturers). This again, only impacts floor exercises.
The only real difference is the inconvenience of having to lift and move the weight if it shifts during the lift, when returning a weight to the floor. But you can always just move your feet.
edit: Just to clarify, I'd recommend round plates over any other shape if all other factors are equal. However, if you have a choice between a gym that is convenient and cheap with octagonal plates, and a gym that is inconvenient or expensive that uses round plates, I wouldn't consider the shape of plates as a major factor in where you lift. Apart from a small difference in a few exercises it is a very minor issue. Don't leave your gym over the shape of the plates - maybe ask nicely for some round bumpers.