Parts can break on either one. The Garand has more parts.
That's pretty dismissive so let me start over.
First, if you mean reliable function as intended, the Springfield '03 is manually operated and therefore can function with much a wider variety of ammo loadings. The Garand's gas system is designed around ammunition with a specific pressure profile. There's wiggle room plus there are aftermarket gas adjustment devices available to widen this further, but you can't go too light and expect the action to cycle. Assuming that's your thing. Use M2 Ball, both rifles work great.
BTW, you can see me using a Garand as a manually-operated straight-pull with ultra, ultra-light ammo (.32 H&R in a chamber adapter) in this video. It ain't pretty, but it can be done.
Three favorite smallarms from my collection. The first is a M1903 Springfield rifle. The receiver was manufactured in 1918, shortly after the double heat t...
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The basic mechanism of the '03 Springfield is Mauser-derived. I've seen more broken extractors on Mauser-type one-piece claw extractors than the Garand's coil-spring powered extractor. That doesn't make the Mauser claw a bad design, but it was designed for controlled feed and you can abuse one by overflexing it chambering single round placed directly in the chamber. The '03's magazine cutoff was a really bad idea IMHO!
The Garand's enbloc clip system is more complicated than the '03 Springfield's simple Mauser box magazine. There's more potential to go wrong, though it usually doesn't on a well-cared for rifle.
I understand the multi-piece striker design of the '03 is considered a weak point, but I've yet to break one.
The Garand fire-control mechanism is considerably more complex than the simple trigger on a Springfield, since it has to include provision for a disconnector. All the same, it's pretty bomb-proof when kept clean and maintained.
Rather surprisingly, I encounter more jams running a bolt action rifle than with a properly-functioning semi-auto. Watch videos of a two-gun match and you'll see even very practiced operators bobble and fumble.
Both rifles are truly great -- get one of each and decide for yourself.