How is the 03 more accurate, faster, and easier to use?
The '03 action is simple a more accurate action in which to build a rifle. That's why when the 03 action was used on target rifles, that's why the 03 action was used to make the Mann Accuracy Devices ( used by the military to test ammo, not just the '06, but the 7.62, the M1 Carbine Round, the 45 ACP, and 22 hornet "to name a few".
It was the choice of civilian shooters for making custom rifles for target shooting and hunting.
It is much faster in rapid fire, being the rifle cocks on opening (as to cock on closing the M1917 uses), the action is smother making it better to use. One should never have to take the rifle out of the shoulder to operate the bolt, its easy with the '03, near impossible with the M1917.
The '03 sights are adjustable for windage, (again, not the case in the M1917). The sights are accurate and positive using the ammo the gun was designed for.
Just look at the scores fired in the CMP GSM matches, and compare the scores fired in the Springfield Match with those in the (other) Military Match where the M1917 is used. This is why the Springfield was given its own match. The cut off scores for the awards are higher for the Springfield then the Military Match, even higher then the cut off scores for the Garand.
To best answer your question I like to have people shoot a practice match (Course A, 10 rounds Prone SF, 10 rounds Prone RF (80 seconds, with a reload required) and 10 rounds slow fire. Shoot the course twice, once with the Springfield, once with the M1917. This will show rather then explain why the Springfield is superior.
Not saying the M1917 isn't accurate, it is, extremely so, if you don't have rapid fire, and there is no need to adjust for windage.