For 2 groups and a yes/no outcome, the square of z is chi-square. So not much difference there! But chi-square can be used for larger designs. I'm not aware of extensions of the z-test beyong 2 x 2.

I was confused at first by the notion of testing for an association vs testing for a difference, but eventually the thread gets into talking about why use Chi Square vs a test for proportions.

I found this in a textbook, that seems to be basically what EdGr is saying above:

"In fact, the chi-squared test of independence is equivalent to a test for equality of two population proportions. Section 7.2 presented a z test statistic for this, based on dividing the difference of sample proportions by its standard error ... The chi-squared statistic relates to this z statistic by X^2 = z^2."

"For a 2x2 table, why should we ever do a z test if we can get the same result with chi-squared? An advantage of the z test is that it also applies with one-sided alternative hypotheses ... The direction of the effect is lost in squaring z and using X^2."