Being an ex-ADT employee I'm biased so I won't advice you about which company. ADT did have good quality standards though and I think they were better than many competitors..
The dog is always a funny mention. What do you do on holidays ? Leave the animal alone for 14 days ?
Your current company should have installed an alarm that sends out a test-signal every 24 hrs. When it is missed once (by the alarm company computer) as message pops up at the operator and should notify you that they have lost contact with your system.
But if the only method of contacting you was that landline......usually they require at least 3 points of contact though and I figure they had your address....so they should have been able to inform you. On the other side, it's also your responsibility as you could have known it wouldn't be working anymore once you gave up the landline.
GSM (or wireless) connections have a lot of advantages like pinballwizard79 says, but it is not as reliable as he writes. GSM services are not up 99.7% of the time by contract or anything like that. They do go down once in a while, although yes it's rare.
For the (professional) fire alarms that are directly connected to the fire brigades over here, more and more ADSL lines are in use. These have the advantage of being continuously "open" for communication (so the status of the system and the communication is checked continuously but of course, these can fail too, so they are backed up with a GSM connection.
Anyway, that's all way too expensive for personal use.
Can't you simply buy a separate GSM dialer over there ? That's how I do it over here. You can program it to dial your cellphone (GSM) phone and it also dials out through a GSM (cell-phone) connection.