Isn't that strange ? I mean cable should be more easily broken than airwaves, no ? Is it because the landlines in Japan are designed to resist and the cell phone tower got power disruption ?
It's because everyone in Japan started sending SMSes to everyone they knew practically before the shaking stopped and that DOSed the network. This happens fairly regularly (e.g. for a few minutes after midnight on New Years, when a large portion of Japanese people send well wishes within the same 15 second window).
Landline phones (pre-ISDN) can get their power from the network, thus mitigating one failure vector.
Also, it is much cheaper to provide enough cable than radio transceivers. Thus mobile networks nearly always run close to full capacity... ever had "network busy" on your phone when dialing in a downtown? So they are easily overwhelmed in emergencies. With landline, in contrast, you always have the line, so it is mostly a matter of installing big enough BX station.