Hope the following steps help you a bit.

Each of your groups with one of the two characteristics you say follows a binomial distribution

X~b(n,px)

Y~(b(m,py)

n=m=1000

The proportions of whom you want to test the difference (large sample)

px(estimate)=X/n ~ N(px,px*qx/n)

Same with py(estimate)

If the samples are independent, compute the difference px(estimate)-py(estimate)

then the statistical function and make it a N(0,1)

The standard error you are searching equals the addition of the two Normals

H0 : px=py

Under the null hypothesis px=py=p, change the numbers of your proportions in the Z

function you created above (careful not the estimates) and you will come up with your Z-test

Keep up