Accuracy goes to the Mauser.
It has a much stiffer more massive action, a more massive bolt, and has fewer "cut outs" in the receiver. The one piece stock with the action inletted into it and fully supported was a major factor.
The Lee Enfield has an action that was always noted for being more "flexible". This is exacerbated by the rear locking lugs, so both bolt and receiver are flexing much more during firing. The LE has always been noted as being more difficult to reload for, due to this flexing causing the brass to stretch more.
The LE's two piece butt stock/fore end, like most such arrangements, just isn't as accurate.
Durability goes again to the Mauser for much the same reasons. The Mauser was always simply a more robust design.
The problems of accuracy and durability were recognized by the Brits early on, which is the reason for the P-13/P-14 Rifles which were a Mauser derivative. It's very probably that had WWI not interfered, the Brits would have been using a Mauser based rifle, instead of the LE.
Reliability is in my opinion, somewhat a "wash".
The LE and the Mauser had enviably reputations in the mud of the trenches.
The Lee Enfield was always a more complicated, "fussy" design, with far more parts.
The LE gets points for firepower with it's 10 round magazine and fast bolt action, but it gets a minus for the rimmed cartridge, and the problems with rim-interlock stoppages.
The Mauser gets points for it's much stronger primary cam-action extraction, and far stronger extractor design.
The LE gets points for its cock on closing design which makes extraction easier, AS LONG AS there's no problem with cases sticking in the chamber.
The LE had a better sights, with windage adjustments and protective "ears".
Bottom line: It's hard to argue with success. Both the Mauser and the Lee Enfield saw extensive service all over the world, in numerous wars large and small, and in every possible climate and condition.
Both stood up well to the demands put on them, and both were resounding successes as service rifles.
It doesn't get better than that.