They are both fun rifles. Lets assume condition is the same, both have good barrels, bolts headspace, all parts included, etc. Then, Mauser, and it does not matter what caliber.
There are several reasons. Mausers are easier on brass, Lee Enfields are horrible. War time Lee Enfield chambers vary considerably, shoulders are different and are huge. You have to segregate Lee Enfield brass by rifle. Bedding will be shot on both, but the Mauser is a lot easier to glass bed than a Lee Enfield. Even after bedding, the average Mauser will be more accurate, though the sights on the Lee Enfield are better. I like the aperture rear on a Lee Enfield No 4, some are better than others, but still better than a notch.
The titling L rear sight on a war baby.
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In theory, the 300 yard side is zeroed with an attached bayonet. Without bayonet the zero is 400 yards, and the 600 yard side is without bayonet. I doubt anyone could remember that under shell or machine gun fire.
A much better rear sight, assuming the front sight blade height is correct. Based on the two American veterans I talked to, I doubt Canadian troops got enough time to sight their rifles further than 200 yards.
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the simple, straightforward typical Mauser
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To a non mechanical enlisted person, this would have taken a month to explain how it actually worked!
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I am going to say, for a battle rifle, both are acceptable, the Lee Enfield, if you get the thing to shoot 4 MOA, that's good for a war time rifle. There was absolutely no consideration of target shooting during the early part of the war. War time standards were get it out the door, now! I have a unissued two groove Savage MK 1*. After bedding it shot a two inch group, but that may have been a statistical aberration. Before I bedded it, it would not hold on a 8 X 11 piece of paper at 100 yards, the foreend fell off when the stock was removed. I did center bed the thing, did not improve matters, it is a four MOA rifle at best.
If you have to have a Lee Enfield MK1, look for the Canadian versions. They are close to pre war fit and finish. They are the best of the WW2 era built rifles, but they are still war babies with the simplifying modifications which were incorporated during the war. The No 4 MKII's are the best built, glom on one if you can find it.
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I am going to say, even though a Mauser is capable of better accuracy, you still have to bed the actions. The worst have been the Yugo rebuilds and the Russian capture. Parts were all thrown in a bin and randomly pulled out and fitted together. However, all my Yugo's responded well except one. It was refinished to like new, new barrel, German K98 receiver. Barrel is not 0.323 interior, it is 0.327! Accuracy is slightly better than a musket. After bedding, testing, I finally slugged the barrel, and there it was. A large barrel.