No and no, but that's pure conjecture since I've never tried a mat.

At work my office has the standard thin commercial carpeting over concrete, which makes for a surface almost as hard as bare concrete. I'm usually in my shoes at work, but I do sometimes kick them off.

I have a standing desk at home as well, where I work almost half my days. I stand barefoot (in my socks mostly) on a thick padded carpet. To keep the carpet clean I have a small area rug over it. Very cushy.

So I've noticed that I'm just as comfortable at work as I am at home. Particularly, the standing surfaces seem to make no difference to the aches in my feet and knee.

I've actually never understood how anti-fatigue mats are supposed to work if you're wearing shoes.

I've been using a standing desk for a couple of months now and will never go back. After a few weeks, I got a nice standing mat and found it to be a great help. This is especially true for me because many of the shoes I wear daily have very thin soles and little support. Yes, I could just wear a more supportive shoe, but at the cost of my excellent sense of style ;).