You do not understand correctly. Compare the ratio of the quadratic f(n) = 1E100 + n2 to the linear g(n) = 1E100 + n. Using n=100 and n=1000 the ratio is effectively 1.0. You need to get to n=100000000000000000000000000000000000000000000000000 before the ratio is 2.
I see your point - we can compare the powers that n is raised to, but without knowing the constant factor we can't know the proportion of the result that it is responsible for.
However, this is in so many ways not my field, so I could easily have completely misunderstood.