The biggest advantage of a landline is Enhanced-911; i.e., the 911 operator is able to determine your name and (more importantly) your address if you call 911 but are unable to give that information for whatever reason. This on top of the fact that you're actually calling your own county or city's 911 call center.
Calling 911 on a mobile phone is very, very different. For one thing, when you first dial 911, you're not calling your own community's call center. You're calling a regional center contracted by the service provider, and they don't even know what city you're in until you actually tell them this. You need to tell them what city as well as what kind of service you need so that they can transfer your call to the right place. If you're unable for whatever reason to complete this initial interaction you're SOL quite simply; but if you are able to give them the information and they transfer you to the actual local 911 center, those guys still don't see exactly where you are. The best they can do is send a request to your service provider, who will send them the location of the cell tower your call is being received by. I know it sounds ridiculous, in this day and age where Google is able to use your phone's GPS functionality to determine precisely when and where you're picking your nose and how long you spent doing it, that 911 operators are left largely clueless, but that's the way it is.
There IS an FCC initiative to fix this; but it requires a complicated set of actions by phone OS makers, service providers, and 911 centers and is rolling out unevenly over a timeline of several years. And of course if you're one of those kinds of people who actually cares about privacy and disables your phone's location services that will probably completely disable the whole system so....yeah.