The correct URL to get user's photo is:
You can change the size to
S or M or L which stands for
Small or Medium or Large.
Most likely your ajax request is cross domain and will be blocked by browser's Same origin policy.
Not 100% sure why its working in chrome, did you try it Chrome's InCognito mode as well ? Could be that you have visited the profile page once and this set some cookies which allowed you to get the profile picture.
Try and visit the user profile page in IE/Edge and then you will also be able to view the image.
To get around this problem, use the URL mentioned above.