Well this is a tough one.
Actually Illustrator doesn't provide the nessasary tools to build sites and interfaces. Its cool for Illustrations, icons and other vector art, but fails horribly at webdesign.
Then we have photoshop. It was a long time the tool for webdesign. The web is pixel based, so its easy to work with photoshop. However, the web is changing. The devices are changing.
I switched some time ago to Sketch. Which is kind of a hybrid. And I am pretty happy.
Not long ago, I had a project where I had to work with photoshop again, and its decreased my productivity rapidly.
I worked with two other on a project and it started with version conflicts. I had CC they had CS6 and they destroyed all my artboards (which are new in CC) . The next problem was, that I was working on a retina mbp and they not. So tl;dr it was a pain.