There are some subtle differences that are detailed here.
The property node allows the reading and writing of a single control within a cluster whereas a local variable and terminal will always refer to the entire cluster. A property node can update the value from a remote location, not on the diagram associated with the panel. If you are using a non-strict control reference, then the datatype of the value may be a variant rather than the actual datatype of the control.
Due to these differences, there are also some performance differences. If updating something like a graph, you would sometimes need to position two cursors, change some colors, and write the data to the graph. In the past this would require two nodes, one for properties and another (terminal or local) for the value. This resulted in two graph redraws. Adding the value property to the existing node and not using the terminal or local will result in one less graph redraw, which may or may not be important for your application.
On the other hand, because they can update a subset of the data, property nodes do not implement the same shortcuts that the locals and terminals do. When updated with the same value over and over, a local and terminal will not redraw the control, but the value property will. Additionally, for controls that are updated very quickly i.e. more than 50 times a second, terminals and locals have the option to amortize the redisplays and save CPU cycles that would otherwise be spent redrawing things you wouldn't see anyway. There is the option to synchronize the display with the diagram updates, and the value property is basically stuck using this synchronized version each time. This is identical to how controls and indicators updated before LabVIEW 5, and it is still how the displays are done on single threaded systems such as any Macintosh with OS 9.x or previous.
To see this, drop a for loop, wire i to an indicator and have the loop execute 1,000,000 times. Initially, update the indicator with the terminal. Run the program and it will take a fraction of a second. The indicator will display 0, a few numbers in between, then 999,999. Move the terminal out of the loop and update with a local. You will see the same. Now popup on the indicator and choose synchronous display -- it is in the Advanced option in LabVIEW 6.x and 7.x. Now you will probably need to abort the VI because it will take several minutes to run because it is drawing every single number to the screen making a nice blur of digits for you to look at. Now, delete the local and use a property node instead. Regardless of the setting of the synchronous display, you will see the display is showing each and every one of the updates.
The fact that the value can be set from subVIs is a great feature, but it will make your diagrams more difficult to debug if you make a mistake. When a string or the indicator has the wrong value being displayed, you need to find the code that did the update. If only using the terminal, there is only one place the indicator is updated, and you can work backwards from the terminal. If using locals, then you have a list of places to work backwards from. If you are passing the control reference to the indicator to some number of subVIs, then you can have many potential "updaters", including dynamic ones. So, while this is a nice feature for modularizing code and separating it from the display, be careful or it will have debugging expenses that you may not want.
The following link details LabVIEW performance and memory management. It includes descriptions of tools for profiling your VIs to see changes in memory and running time.