The composition of the eraser does cause some differences in how the graphite is removed, but in general I've found that a dabbing twisting motion is best regardless of what the eraser is made of.
Soft putty erasers I find are the best for soft pencils and a hard grit eraser best for H4 and harder, but be gentle as it can shred the paper fibers
The Staedler Mars Plastic I find is a good general purpose eraser.
And a final tip, keep the eraser clean, I find rubbing the built up graphite off with your thumb to be a good tip prior to using it.
