Difference vs. Ratio of evidence in sequential sampling models
Unless I'm misunderstanding what you mean, ratio of evidence is actually a terrible method because that would end up with an immediate decision as soon as any evidence is encountered for either side, giving a ratio of infinity for that side (something/0 is greater than any finite decision threshold).

Try Gold and Shadlen 2007 for a review http://synapse.princeton.edu/~sam/gold_shadlen07_annu_rev_neurosci.pdf