Hello Beth,
I just read the answers above and found they didn't hit the nail on the head.
Normally they are interchangable, for example
楼市让人发疯,让人抓狂
The property market drives us crazy.
However 抓狂 implies that there is nothing you can do about it when bad things happen, or you are in a situation that goes beyond your ability or experience to handle it. in this sense, 抓狂 can't be replaced with 发疯。in addition, 抓狂 foucus on inner feelings and 发疯 is more of outer behavior
每次客人来,我小孩就发疯
My kids act up whenever guests come. (outer behavior: they behave badly by being very active and noisy or throwing tantrums )
每次摆不好拼图,我小孩就抓狂
My kid goes crazy whenever he fail to solve his jigsaw puzzle (inner feelings: He feels irritated or angry )
发疯 literally means someone who is mad or insane is seriously mentally ill so that they cannot live in normal society, in this sense, they are not interchangeable, we can't use 抓狂here.