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I wouldn't say that the question is one that can be answered in general, since to get the rate, we have to compute $$|M|^2$$ and integrate over phase space. Generally some diagrams will contribute more or less to the computation.
For instance $$e^+e^-\rightarrow e^+e^-$$ gets contributions from either an intermediate photon or $$Z^0$$ particle. When the energy of the initial particles is very small, the contribution from the intermediate $$Z^0$$ is extremely small.