Depends on the color, season, year, and individual bag.
I owned many 03 citys, lilac, dark turq, blue, red, black, caramel....all had very smooth, matt, almost moist leather. Loved them! As I recall, most had very thin, fine, but durable leather.
The only 03 I have now is a caramel which I love. I sold the rest as I prefer twiggies, which didn't come out til 04.
Marron 04 is very thin like the 03. My rose and pumpkin are super silky but tend to have more distressing than the 03's, and are less matt. May have had more glaze originally.
Both years were wonderful. The only early bags I don't care for are the flat brass classiques with the papery leather. Can't remember if they are 02 or 03 S/S.
And S/S 05 if fantastic with plump, smooshy leather, while F/W 05 had thin, veiny, dry leather. Too bad cause the colors were great.