What are the pros and cons of two AC systems vs a dual zone system?
A dual-zone system is one heating element and/or AC coil serving two separate ductwork segments. The extra cost of a dual-zone system as opposed to a single-zone system is in the dual-zone temperature monitoring/control panels, and a system-controlled diverter that sends the air to the side of the system that needs it (or both).

The upsides:


One interior and one exterior unit to buy/maintain. Drastically reduces most routine maintenance costs and generally increases MTBF.
Easier to balance your home's ventilation; you don't have to worry about the relative heating/cooling capacity of two units versus the space they're expected to cover.
Dual-zone systems usually have a "master/slave" control panel arrangement allowing the "master" panel to control both zones while the "slave" panel can either also control both or only control the secondary zone, possibly with additional restrictions like max/min temperature that can be set on the master panel.


The downsides:


No backup; if something on the one unit goes, there is no heated/cooled air anywhere in your home.
Impossible to differentiate the electric costs of you versus an upstairs tenant.
Longer ventilation runs to the second zone, depending on home design; the second zone needs vents and returns run from the main unit to a usually distant part of the home. These longer runs will not be as efficient.
To supply ample heated/cooled air to both zones at once, the unit must usually be a bit beefier than a comparable single-zone system, to compensate for inefficiencies and maintain desired airflow when both zones are being ventilated.
You cannot have the heat on in one zone and the A/C on in another. The entire system must be set to heat or cooling, meaning if your tenant likes it substantially warmer or cooler than you do, the ability of the system to provide the proper temperatures can be limited at times.


A dual-unit system will have two separate single-zone HVAC units each controlling one area of the home (upstairs-downstairs is common in new construction, as is having a second HVAC for a new addition).

The upsides:


Having a backup system means at least some of your house can still be heated or cooled in the event of a failure of one unit.
Vent runs can usually be shorter, as the units can be strategically placed in new construction for the most efficient ductwork layout to each zone.
Each unit can be smaller than a single unit for the whole house would have to be, meaning the exterior units can be located in tight spaces or more easily hidden behind shrubs.
By hooking the second HVAC along with all upstairs circuits to a sub-meter, you can easily determine (and sever) the electrical costs of an income property.


The downsides:


More expensive to put in than a single unit, even a dual-zone. Two 1-ton units will cost more than a 2-ton.
Maintenance costs also increase; with two units the MTBF of a single unit in the home is halved, meaning on average you'll have to call the repair guy twice as often.
Less centralized control. There are some nice thermostats that can communicate wirelessly (usually as part of a whole-house automation/alarm system), but basically each unit will be its own completely separate system and to balance the temperature in the whole house you must go upstairs and down to fiddle with settings.