Both sights are model 1898 altered to 1902 format.  If one of the rifles has an 1903 cartouche the sight is a replacement.  Given the 1898 altered to 1902 was an analog of the 1902, as made, sight the replacement is "model" correct as a replacement but not for as made.

The slide up peep was added when that sight was altered to 1902 format as all 1898 sights were made sans that peep.  The other sight simply didn't receive that mod.

Cheaper to buy a sight than fix that.  On a good day a loose sight can be had for $26.  On a bad day they go higher.