I agree - the Lee-Enfield and Ak47 are too different to make a fair comparison - remember to control your variables. The US purpose-built sniper rifles are based on the same or very similar weapons so they make the closest match of the in-field weapons that I've found. What we want for a real-life comparison is the exact same weapon and round differing only in the reload mechanism.
The tldr result is that there are many more significant factors than the energy-loss to the reload mechanism that affects the range of a weapon.
Note: the Lee-Enfield Mk1 is the first rifle I trained on... and I keep finding rubber versions in movies.
The L42A1 was the sniper version fired a 7.62mm NATO round at a muzzle velocity of 838m/s and an effective range of 730m.
Bog-standard Ak47 fired 7.62mm round at a muzzle velocity 750m/s, effective range: 400m (300m full auto)
... "effective" is the range at which you are "reasonably" accurate according to some test done by someone, probably a manufacturer. Notice that the Ak one goes down by 100m just switching to full auto ... i.e. the reduction is due, primarily, to the continuous jolting you get firing it.
If we are going to try to compare them...
Bog Standard L-E fired a 7.54mm (0.303) round at a muzzle velocity of 744m/s, effective range: 503m
... despite a similar round and a lower muzzle-velocity, the effective range is longer.
The lower velocity suggests, all other things being equal*, that less chemical energy was supplied to the bullet in the LE than in the AK ... which would support a conclusion that the bolt-action mechanism is lossier (see note for M41 vs M40 below).
Going to wikipedia (fwiw: their citations in the entries are dodgy but hey ho)
M14: rnd: 7.62mm NATO, mv: 850m/s, eff R: 460m
M21: rnd: 7.62mm NATO, mv: 853m/s, eff R: 835m
... these are both gas-operated, rotating bolt, semi-automatics - yet there is a huge increase in the effective range for the sniper version. It could just be that the sniper version has a bipod and a good sight. We really want to be comparing maximum ranges... maybe the muzzle velocities will reflect the question better?
(The wiki entry for the M25 has a max range of 900m ... which is rubbish, I'd buy that as "effective range" though. The max range is how far the bullet goes horizontally at an elevation of just under 45deg**. at sea-level mean TP. i.e. 1000s of meters. There wasn't enough information in the entry to compare with the other two M14-based weapons, so I left it out.)
How about the bolt-action?
M40: rnd: 7.62 NATO, mv:777m/s, eff R: 900m
... notice the
decreased muzzle velocity with the same round for a bolt-action rifle? Again indicating that there is more to figuring the range than the chemical energy applied to the bullet.
Which is the takeaway lesson here for OPs question.
Yes - the automatic action does divert some of the energy that may otherwise have gone to the bullet (and the recoil), and this will affect the range. However, there are other factors that are more significant than this effect... it's probably something the manufacturers would consider as part of the finer points of weapons engineering.
This has been demonstrated in-thread by consideration of the physics involved, consideration of actual in-field weapons, and the opinion of a trained army sniper, which all support this conclusion.
I'd call that a slam dunk. :D
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* but all other things are
not equal. You want to see how hard it is to compare two weapons see
http://en.wikipedia.org/wiki/Comparison_of_the_AK-47_and_M16
... comparing automatic rifles. Ak47 is compared with the M16A1.
Note: "effective range" means "range at which the desired end is achievable with reasonable accuracy" ... which is almost like not having a definition at all. Who decides what "reasonable" is for accuracy for example? The "desired result" could vary a bit from weapon to weapon too - do you just want to hit the target or kill them? The Ak47 has a spread of 15cm at 100yds while the M16 has 10cm (can't tell if that's mean or what)... it's a wonder anyone misses. Dow the page there's a table nd some commentary - basically the lower accuracy of the Ak is due to the recoil from the heavier round.
** Oh OK - likely less than that. As close to the with-drag max-range elevation that can be reasonable sighted to a target.
http://www.exteriorballistics.com/ebexplained/5th/36.cfm