There are plusses and minuses everywhere. What makes the baddest sniper rifle of all time? Accuracy? Range? Power? Physical size? Funny, you mention source as the military has often gone to the private sector to source weapons. Honestly, I don't think the baddest sniper rifle has been built...at least for the military. There are great rifles, but better options not used. So I'll include M24/40's and M70's.
Breaking it down, the 1903 is for all intents and purposes a Mauser. In the U.S. Inventory, we have yet to optimize a military bullet for great long range shooting. Previous to WWII the Germans optimized the 7.92x57mm cartridge. The bullet remained stable out to 2500m While the optimization was intended to spruce up machine gun performance, it worked exceptionally well for the sniper role. The drawback to this was a lack of firepower in case of having to fight your way out. 5 rounds and done. So it kind of ends up on the same pile as the 1903. It could shoot farther due to the ammunition, but could only hold 5 rounds. Post WWII until very recently, MOST bolt action sniper rifles were limited not only by rounds but by the ammunition. It's like we improved in that we kept the programs, but remained with our heads up our asses, thinking 30-06 and .308 were the "go-to" cartridges. Lots of cartridges came and went,but were turned away as "not mainstream". The myth that the 30-06 was the "world standard" prevailed and we did not improve. So, IMO, anything mentioned here is too limited to say "best". This includes the Mauser (and variants), 1903, M24/40, and M70.
Stepping back in time to WWI, when the Enfields and Mausers battled each other we find that the Enfield had the range, due to a better bullet design at the time., Accuracy was quite acceptable and the Enfield held ten rounds. This carried on through WWII and other conflicts all the way up to 1996. But, still it's a bolt action. And while it holds ten rounds it still has to be cycled manually. Without a mass of rifle fire, it's too slow in case of a "fight your way out". scenario.
In 1911, the Swiss felt they needed to upgrade their inventory So, they built the 1911 rifle and introduced the GP11. For all intents and purposes, this is the single best .30 cal cartridge of all time. Later when the 1911 rifle was replaced with the K31, they maintained the cartridge. It's accuracy and range are exceptional. Although it does not have the range of the WWII German 8mm.
Moving to the semi-auto's of yesteryear, the Garand was good but not as accurate as it needed to be. I'm talking a system that has first round hit capability at 1k. It's successor the M14/XM21/M21 was better for accuracy, but not up to the standard the bolt guns held. 1k was not always readily attainable.
So we move to the European side. The two biggest contenders for this type rifle were H&K and FN. Initially, when the FN-FAL rifle came out the British used a handy li'l 7mm called the .280 British. With it's 140 gr. bullet, it was capable of 1k. But, it was slower than it's little known cousin, the 7x49 Venezuelan. Here was the cartridge/rifle combination that truly brought into being the consistent 1k range. The cartridge was essentially a .300 Savage necked to 7mm. In the U.S. it was a wildcat called the 7mm Int'l rimless and 7mm Olympic. In a standard configured military action based sniper rifle, this was about as good as it gets. It launched a very high BC 140 gr. bullet at 2850.
I saw the PSG1 being used by the Germans when I was over there, but the 7.62 cartridge limits it. Also, I didn't see it as being as accurate as the FN-FAL.
Fast forward to the AR types. You have the -15's and rounds that went in them, and the -10' that run .308 sized cartridges. Of the -15's I found that a 6.5G in a MK12 platform was the best range and accuracy. Better by far than the Mk12 chambered in 5.56x45 using Mk262 (77 gr. SMK) and even single fed 90 gr. SMK. But, these only saw limited use and the mainstream army does not seem interested even if it works better.
Of the -10's, the limiting factor is the same as the bolt guns. No one in the U.S. supply system is interested in making changes. At least until those who want it, go and do it. As I understand there are SOC units are using the .260 Rem with high BC bullets (to get that range needed) in a -10 platform. I know what the success capability is of this cartridge and rifle combo. As Buffalo said, it's a great feeling when you know you can pew, pew pew, your way out of trouble if it starts to overwhelm you. The only drawback to this cartridge/platform combo is you have to drive it near perfect to get the performance you want. The different impulses make staying right on target a thing you have to focus on. Weight over the -15 platform is also a big factor.
As far as the .50's, .400's, .375's and .338's one is hard pressed to find the kind of supreme accuracy you need to get first round hits well beyond 1k in a semi-auto platform. Even with good brakes, the ability to drive one in pinpoint accuracy situations is difficult.
All that said, M110 platform, chambered in .260 would be my choice. Followed by a 6.5G in a -15 platform of my liking.
