Accuracy is a relative thing. It is usually measured in group size, and minute-of-angle.
For example, if a Lee Enfield made 2 inch groups at 100 yards, 4 inch groups at 200 yards, etc., you could reasonably expect 12 inch groups at 600 yards. However if the rifle actually did 8 inch groups at 600 yards, it could be considered "more accurate at 600 yards".
When a bullet is fired, it actually is very slightly unstable, and tends to yaw a very tiny amount around it's axis. Depending upon the design of the bullet, some have greater stability as they slow down a bit, which would be farther down the range. This is known as "going to sleep". The lowering velocity decreases the yaw around the axis of the bullet, and it flies truer. This would account for the increased relative accuracy at longer ranges.
There is also a factor known as "compensation". Simply put, when you fire a rifle the barrel actually vibrates. Depending upon lots of factors, a barrel may simply shoot better at different ranges, and whether the vibration of the barrel is sending it down, or up in the vibration cycle. If you changed the length of the barrel, this vibration cycle would change, and affect accuracy.
From a personal point of view, I always preferred the No.4 rifle for ranges up to 600 yards, but used the No.1 Mark III for ranges of between 600 and 1000 yards on the range, because I believed (and I am not alone on this ) that the No.1 Mark III rifle compensated better at the longer ranges.
This is a brief explanation. You have to look at accuracy relative to range of the target. For example, I have a Stevens .223 that shoots 60 grain Hornady handloads in the 9/16 inch area at 100 yards, about 1 1/2 inches at 200 yards, still stays about 1 1/2 inches at 300 yards, and about 3 inches at 400 yards.
Lets say this rifle does 3/4 minute of angle. (although a minute of angle is slightly over an inch, we will use one inch here). At 100, 200, and 400 yards, I am still about 3/4 minute of angle even though I am shooting larger groups. However my 300 yard groups are in the 1/2 minute range, so I could say that my rifle is more accurate at 300 yards.
Hope this helps.