With new technology, Offset Printing has changed. In particular the Web press has changed and it's the run length more than the quality that will determine which press (Web or Sheetfed) is used. You are likely, however, to pay a slightly higher price for the sheetfed process, as these presses will very often have more printing units which can be used to give gloss or protection to the printed sheet or to print your special colours.
Next: Web Offset Printing