From a pure design point of view, the '03 is inferior to the original Mauser design.
The Mauser '98 design is one of those rare "perfect" designs. There is NOTHING that can be done to "improve" the '98 design, and all changes since Mauser invented and perfected it, are to allow it to be made cheaper or faster.
When the '03 was designed, the basic Mauser design was modified to what the ordnance department thought an American service rifle should be.
In order to do that, they actually produced a design that was inferior to the deceptively elegant '98.
The Mauser's bolt lock is a very robust, large pin with a strong spring, both of which are completed covered by the bolt shroud. These just don't give trouble, no matter what.
The '03's bolt lock is a tiny, flat piece of steel with a very tiny spring, both of which are mounted on the side of the bolt shroud, and completely exposed to dirt, grim, and weather.
They fairly regularly gum up, rust, or wear and fail to properly lock the shroud.
The Mauser extractor's front end rides in a dovetail groove. The harder the bolt is pulled, the tighter the extractor grips the case head.
The '03 extractor rides in a non-dovetail groove, and can slip up out of engagement with the case head.
The Mauser's safety is a one piece chunk of milled steel, and is easy to disassemble.
The '03 uses a multi-part assembly with an exposed spring and plunger and requires tools to disassemble.
The Mauser uses a light one piece firing pin with a small, light cocking piece.
The '03 uses a heavy multi-part firing pin assemble, with a massive, and more or less unnecessary cocking piece grip knob.
The Mauser uses a simple, strong ejector/bolt release assembly.
The '03 uses a smaller, weaker ejector, and the complicated magazine cut off/bolt release. To be fair, the cut off concept was still valid in 1903.
The Mauser receiver is deceptively simple, and has a very strong rear bridge.
Although hell-for-strong, the '03's receiver is complicated, and has a weaker rear bridge.
The Mauser stepped barrel is easier to bed, and the bedding system at least potentially offers better accuracy than the tapered '03 barrel and it's tendency to "wedge" in the bedding.
The Mauser stock, and particularly hand guards are stronger than the '03, and offers a better shooter's grip than the skinny straight-grip '03 stock.
Overall, the '03 was superior for the quality of workmanship. The Mauser suffered from manufacture during loosing wars, and quality ran from excellent to "last ditch" poor.
The '03 was always uniformly excellent.
The Mauser sights were too simple, and should have had a windage adjustment. Although simple and fool proof, the sights prevented the rifle from reaching it's full accuracy potential.
The '03 sights were too complicated and fragile, and were incapable of repeatable settings since there were no "clicks" or other positive means of adjusting them.
In fairness the '03 sights were state of the art in 1903.
In sum, the statement that the Mauser was a battle rifle, and the '03 was a target rifle, does have a certain truth. This is understandable, since the period from around the turn of the century up until the era of the M-16, was the era of the "target shooter's" in Army ordnance.
They insisted on accuracy almost to the exclusion of all else. The well-documented development history of the M1 Garand gives fascinating insights into this attitude. There was strong resistance to the M1 because it wasn't accurate enough, and would lead to the old horror of the "target shooter's": Soldiers wasting ammunition.
In the 1903, they got the target rifle they always wanted, and it did serve very well through two world wars, the "banana wars"
and into Vietnam.
It was superior to the Mauser only because of the quality of materials and workmanship.