As someone else mentioned, I would investigate cork flooring. What I've seen looks great, mutes sound, and you could still find the pins. I also do a sweep with a magnet from time to time!
At one time, I was in a converted garage with cement so I had the epoxy flooring put down. That was awesome! Although I don't think you could do that inside the house.

We had luxury vinyl installed and I love it. It's easy to keep and find dropped needles and pins :)

I have white ceramic tile in one area of my sewing room and carpet in the other area. (two rooms opened in one) I like the ceramic tile area the best. I have the cushioned floor mats on the tile by the ironing and cutting tables. The carpet absorbs the noise and gives some cozy to the room. The tile gives a bright clean look.

I would go for wood .Clean up is easyer.

Concrete and it's not bad. I may put down some laminate or vinyl to soften it up a bit, warm it, but my chair rolls easily and dropped pins are easy to find. It looks like just about everyone recommends getting rid of the carpet :)

I have tile in sewing room. However, I am always cold and I put in carpet. I love it! :) I will say it is harder to clean but much nicer on my feet and to keep me warm. :)

Sewmary's right. Carpet is a nightmare. I hate, hate, hate mine for all the reasons Laura said. Would rip it up & put down wood in a heartbeat if I could afford it.

Absolutely go with a wood floor! If you have a rolling chair, you will have a much easier time using it on a wood floor. I actually broke a rolling sewing chair that came with my machine cabinet, because of the fact I have carpeting on the floor and it was so hard to push that chair around!!! Now obviously there are carpets with shorter naps which may not pose a problem, but if the carpet has much of a nap at all you will have to really push to get that chair to move where you want it to go!

Love my hardwood floors DH put down.
Just use swiffer for threads and magnetic extension wand for needles and pins and they show up easily.

I have short loop carpet in mine. It was there when we bought the house. Works great! Things don't get lost in it, my chair rolls just fine, and it's warmer. I think it muffles sound as well.