Here is a link to an EXCELLENT explaination of train brake systems:
http://www.railroad.net/articles/railfanning/airbrakes/index.php
I use both brakes... but it really depends on the train I'm running as to how I use them; alone and together.
If you are operating a switcher loco alone or with only a few cars, the independant brake alone works way better. With a long freight train, that same brake alone is virtually useless.
You can use the independant brake to control low-speed acceleration or braking. If I want to stop a train exactly in front of a signal or at a station platform, I'll use the train (automatic) brake to get down to 10mph or less and then set the throttle to notch 1 or 2 and control my final stop with the independant... nice and smooth. I don't even bother with the train brake on RDC's or trams.
The independant brake can also be used to control accelleration. Short lightweight passenger trains or RDC's have a tendency to be over-powered and riders really appreciate a smooth depart. While this is not so important on a freight train, the independant brake can also be used to some extent to help control wheel slip.
Since the independant brake only controls brakes on the locomotive, it reacts immediately, unlike the delayed action of the train brake, which is very cool when you just want to trim 1 or 2mph off your speed right now. It can be used to augment dynamic braking, creating even more drag at the front of the train... just be careful not to overheat your loco brakes and possibly set a fire.
Coupler slack can be controlled with the independant also. When backing a train to couple with cars, you can use the loco brake to 'stretch' your train and reduce the resultant impact. This is also nice when starting a train uphill; release the train brake with the loco brake applied and allow the train to stretch before trying to move.
Of course, all these examples apply more to the real world than to Trainz (which is WAY more forgiving.) But, if you want prototypical operation like I do, that's what I do.