I never had any issue with color difference in browsers. (EXCEPT IE). IE may change shades to some extent.
The only issue I have is with different monitors. I use LG Flatron CRT monitor for designing. And when I view the same design on my HP Laptop, all the shades below 10% of that color are invisible. i.e. if I give a box shadow of 10-20% black, it will hardly be visible on a laptop screen. Colors tend to loose their contrast and saturation.
I would like to know from fellow Authors, which monitor screens you prefer? LED, LCD, TFT, CRT etc.