Bit of history that I've read...I own a WW1 version of the Lee, and a BSA modified or sporterized version of the Eddystone M1917.
The Lee Enfield is considered by many gun historians to be the best "battle" rifle of its era...and even best "battle" bolt action of all time. One reason is because the chamber was made to somewhat loose specifications, and thus it wasn't particularly fussy about ammo, which was made in numerous factories during the war, and to varying degrees of uniformity. Also, because of its design with a rear locking lug it was a relatively fast action to unload and chamber a new round, and it was a relatively simple matter to correct the head-space. They were never known for particularly great accuracy, albeit some did earn their keep as sniper rifles.
Springfield was sued by Mauser for patent infringement with the 1903, but IMHO the Enfield is a closer knock off the '98 Mauser action. The first version was a "Pattern 13" designed for the .276 Enfield, prompted by the Brits experience against the 7MM Mauser during the Boer War. When WW1 broke out, that caliber was dropped in favor of the .303, for which there was already tons of ammo. As mentioned, the ten round clip was a real winner in the trenches.
My experience with my P17 as per BSA might be informative for some. Very accurate, surprisingly so. (I once shot two targets at turkey shoot with it against 9 others...100 and 200 yd, and won both, up against some pretty fancy iron at the time!) That said, short version - BSA didn't do a real good job of machining the actions, I assume, in removing the military sights. This caused a serious misalignment between front and rear mounts, and bent the tube on my scope...which Bushnell very kindly repaired no charge. These rifles are a prime candidate for Burris Signature rings, which will prevent this from happening, and with offset shims that are available for these rings, and a bore sighting tool, proper alignment can easily be attained in a matter of minutes. (IMHO all older rifles are similarly candidates for these rings for the same reason, as manufacturing standards back in the day were a tad less precision than modern equipment now affords us. Misalignment is very common due to this, and can wreak havoc with a scope!!!) I put a Dayton Traister trigger in mine, but there are more options now than there were back then. Highly recommend some kind of upgrade to the original two stage, will make a better shooter out of any of them. I never went for the #### on opening conversion, wasn't a concern for me.
Lastly, whatever you do with one of these, get a real gunsmith to perform the mods...especially if it comes to drilling and tapping for scope mounts!!! I've seen a couple trainwrecks in this department, which is sad when it comes to fixing up a hunting rifle for the long run. Some times the Signature rings can overcome this, fortunately.