Digital phones use less than half the power of the old analog phones, hence the much longer battery life for similar usage. My old phones would cause feedback through my computer speaker systems when I used the phone while sitting at the computer. I doubt there are many (if any) analog phones in use any more.
While I find it hard to believe a single modern cell phone could cause interference in an intact airplane, I often wonder if several hundred phones all vying for a signal could, in fact, put out enough power to induce signals in an antenna cable or other cable, especially if there is a shielding defect or loose coupling. I don't think it's beyond the realm of probability, and I wouldn't want to find out the hard way during a Cat III approach...