The biggest difference between Curves and Boost is acceleration/deceleration. But I'm sure you already know this. Curves allow you to slowly ramp up or down. Boost is literally changing the dead zone which means it's totally skipping the ramp up and is pretty much instantaneous.
I had a graph somewhere on this, here you go... I think I've shared this with you before though. As a none developer, this is more my type of lingo.
Boost can be useful for some low Turn cap games or games that utilize timed acceleration. IMO though, it's best purpose is for trying to make a dead zone work with an unsupported game or for Vehicles, which are also unsupported.
The real difference between Boost and Ballistics is Boost is instantaneous from point A to point B. It allows you to manipulate the starting point of the right stick. So if you pick up your controller and slowly move the right stick you will feel a certain amount of play "Dead Zone" before your movement actually registers on the screen. As you push harder on the right stick your movement speed will increase. Boost allows you to completely bypass that dead zone (if you wish) and you can pretty much choose the starting point of your right stick movement. So if you crank Boost WAY up, it's just like starting your movement at the point where the right stick is immediately pegged. Ballistics allow you the same benefit except you can slowly ramp up or down to the desired speed instead of getting there instantaneously. Also Boost only works as acceleration, where ballistics can also slow your movement down if so desired.
Think of it like an electric and a combustion motor.
- Unless you're using a VFD, Electric power is instantaneous, as soon as you turn it on, you have the max output that your motor can draw from it's power core. - BOOST -
- Combustion motors have a lot of mechanical parts that take longer to build up torque. - Ballistic curve -

Now ballistics can be instantaneous obviously, if you make a ballistic like the electric graph above. Which is EXACTLY what you guys are doing.
So basically, for the purpose of what you guys are trying to accomplish either way should work. Which works better depends on which can be finer tuned. For that answer you would need OBsIV's input.
I can say that dead zone compensation is why boost pretty much exists. So in theory that should be the "go to" method for making adjustments. That is why I suggested using the method I posted for finding and setting dead zone. It's the best method I currently know of and eliminates a lot of trial and error you play with the guessing game of adjusting on the fly.
But theories exists to be broken one day.