Hey Ranger SVO.
What kind of parameter, measure are you looking at? (For example, the mean? Median?)
If you are doing surveys with stratification then the best linear stratification measure with uniform cost constraints (a cost function is used to introduce how much it costs to actually do a survey/experiment/whatever) will be based on this:
This gives the best stratification policy (i.e. the number of samples required for each strata) to get the smallest variance with a uniform cost function (think of it as it costs the same amount resource wise to do one survey at any school).
In terms of difference between the two means, you will need to solve for t-distribution where t_a/2*SE(x_bar-y_bar) < v where t_a/2 is the information for the quantile with alpha/2 in each tail and SE(x_bar - y_bar) is the standard error x_bar - y_bar (given in the formula for t-distribution) and this is just a function of your variance above.
You then solve for a particular (n1,n2) combination and choose any value that satisfies the inequality.