Most of the advantage is aerodynamic. If one moves from riding on the bar tops to the drops on a road bike, one immediately sees an increase in cadence, and speed, at constant effort - and this is all abput wind resistance.
However, being rotated more forward also offers some advantage in recruiting different muscle groups. Time triallists will tend to be low, and forward, so that their centre of gravity is almost ahead of the cranks.
As for the saddle, it all depends on how low you go and how you are set up at the moment. If I were you I'd proceed in small incremental adjustments and, at each stage, review whether you're still sitting comfortably. You certainly don't want to shift your weight from your sitbones to your perineum.
If my saddle position is correct, more reach puts less weight on my hands, makes less strain on my back, and in general just feels a lot more comfortable. I have a number of riding buddies who fixed their back pain problems by lowering their bars and extending their reach.
Many Thanks for the replies - sounds like good advice
One thing - leaning more forward will put LESS weight on my hands ?
No, people will say that because they're imagining crouching above the seat, balanced with their butt further back. Being balanced there would be no weight on the hands so they conclude that moving the seat back and leaning forward more reduces the weight. It confuses people because it's clearly not true. We normally sit on the saddle. Leaning forward more puts more weight on the hands.
The reason that moving the saddle back sometimes reduces weight on the hands is because it's one factor in a more complex, dynamic situation. When the fit is good, weight is distributed comfortably. Force vectors balance against the weight at angles appropriate to our physiology. Additionally depending on flexibility and core strength, leaning forward can recruit core muscles which take some of the strain from the hands at a (compared to) more relaxed posture.
As Chasm mentioned the more aggressive postures are more comfortable and effective for more intense efforts, but less comfortable for easier efforts. The amount of reach is curious because depending on the overall configuration it can lead to different, even seemingly contradictory objectives. In a so-called French Fit position with high handlebars for instance, a longer reach is desirable because you're sitting up with straighter arms and it feels easy and relaxed with the arms at close to 90 degrees at the shoulders.