I also use NextAlarm, with cellular communications as my primary method. I have zero complaints about them as they have come through in every situation.
I do agree with sic that cellular is the way to go. When my home was broken into several years ago (before I had my alarm system), the first thing they did was cut my phone line on the exterior of the house, probably assuming it disabled the alarm. Luckily, they didn't cut the coax cable as well, and my computer was able to email me. Now, I use cellular as my primary communication. Let them cut the cables and make an assumption that they have a long time in the house before anyone shows up (even see phone fault on the keypad if they look close enough), but be surprised when NextAlarm gets the police there quickly.