My opinion would be that changing weight distribution and changing springs and sway bars do different things to improve handling, although there is also some overlap.
Bringing the mass of the car as close as possible to a point half way along the wheelbase is an important objective; NOT just a 50/50 weight distribution. The point here is to reduce the polar moment and make the car change directions more quickly. Imagine carrying a barbell on your shoulders and trying to turn quickly, the more weight on the ends of the bar, or the longer the bar, the more difficult it is to turn, even though the weight is distributed evenly. Bring the weights in closer to your shoulders and you can turn quickly without "overshooting" from the pendulum effect.
While the engine and transmission are the most massive items in the car you can also get cumulative results from a number of smaller changes, like relocating the battery, removing bumpers etc.
The use of different suspension components can also control weight transfer under either braking or cornering and so has similar benefits, but the main objective here is to keep the contact patch as flat as possible on the road so as to get the most possible grip. This is more important after the car has taken a "set" in the corner and is in a steady state cornering mode, while reducing polar moment is most helpful in transitions, i.e. turning into a corner or a series of esses, weight distribution helps both types of behaviour.
Finally, reducing unsprung weight and rotational mass helps a bit too.
All the above just my opinions, please discuss, differ, refute, contradict or otherwise!
Simon.