How do security alarm systems measure zone resistance?
I cannot say for certain if current source or voltage divider is used.  You could put an ammeter in series with a zone circuit, open and close a sensor, and see if the current stays constant.   

EDIT :   The OP question about EOL is "end of line" resistor on a zone loop.

What I Can say is, what are some of the design criterion that a manufacturer might consider. 

Using a current source appears to be the better method, unless the power budget would not allow for current source method.  Current source method would be expected to consume more power than a voltage divider method . A security system has to operate from battery power during power outages. Consuming more power because the “current source” method was chosen will reduce the time duration for operating during power outages. 

WHY CHOOSE Current source method :  Systems designed to operate with User Connected Wiring need to account for induced extraneous noise. Installation contractors don’t think about noise suppression , twisted wires, proximity to other equipment, nor wire length. Using a current source to power the sensor generally results in a higher noise immunity. I won’t go into why current sourcing in this manner results in higher noise immunity. But if one wants to know about noise immunity, just look into 4-20 mA control loops (lower impedance is one reason).

One link to current loop's noise immunity is , http://www.ni.com/newsletter/50262/en/ ,  "Because all the current that flows from one lead of the power supply must return to the other, current loop signals are immune to most sources of electrical noise "