I prefer silk; I've bought many from Jinglebobs and have two on me now.

Here are some numbers. I'm comparing a 20" silk with a 21" cotton, both good quality. The cotton weighs 31.4g, and a single silk weighs 10.8g. So the silk is 1/3rd the weight.

I normally fold these in half twice, and then in thirds concertina-style, to make a pad that measures about 3.5" square. This then gets carried in a back pocket until it's well and truly compressed. The cotton ends up about 0.75" thick. Stacking them up, 3 silk are well under the thickness of 1 cotton, and 4 silk are slightly over. I'd say the silk was 1/4th the thickness.

I also have some 35" silk. These I fold in halves then in concertina quarters so the pad is about 4.5" square. One of these larger silks weighs 30.3g, and two of them are about the same thickness as the 21" cotton. (I also tried the 42" silk, but found it inconveniently large, and won't include it in this comparison.)

The 21" cotton will hold about 120g of water; after roughly ringing it out that went down to 84g. For 20" silk the figures were 33g and 24g respectively. This suggests to me that the absorbency depends less on the material and more on the thickness or weight. 3 or 4 silk together weigh about the same, have about the same thickness, and have about the same absorbency, as 1 cotton.

The cotton is a lot cheaper. A 21" cotton is usually around $2, the 20" silk is $8. This does make you feel less inclined to use the silk for things which might get them dirty, or to cut them up, etc. If you actually carry 4 silk then that's $32 or 16 times the price to get the same absorbency.

Overall for me the silk is a clear winner. The 35" is the same weight and half the thickness as a 21" cotton, but much more versatile because of it's much larger area. The diagonal is around 50", which is long enough to go around any part of my body and leave enough to tie, which can be important for first aid, or if you need a belt, or whatever. It's big enough for a sling for an arm, which 21" isn't. If you need to cut it into 5" squares to use as toilet paper, the silk gives you 49 sheets and the cotton only 16. More is better. If you need thickness for insulation, you can double it up, or quadruple it.

The 20" silk doesn't perform as well as 21" cotton, but being 1/4th the thickness and 1/3rd the weight makes up for it. They are light and thin enough that I regularly carry one in a shirt breast pocket, where cotton would be too much. You can carry three or four silk in the space of one cotton, and that gives you more options for using them - it matters less if you get one dirty if you have others. You can bind three or four wounds instead of just one, etc.

Nowadays I like to carry a 35" in my right back pocket, and a 20" in my left back pocket with an emergency poncho. They are thin and flat enough not to be uncomfortable to sit on, and it's not the end of the world if one gets pick-pocketed. (The poncho is thin plastic for water-proofness, which is sometimes good to have too. It weighs 48g and is about 0.5" thick. There isn't room for that and another 35" silk, but there is room for the 20".)