In the brocho of “hakol yoducho” Shabbos Shacharis, some siddurim have “sheboro bemidas rachamim” while some have “sheboro bemidas HOrachamim”. Why?
So far all I've got is lists of siddurim, not a real answer.
במדת רחמים seems to be the older and more widespread version. Various old siddurim on Hebrewbooks (both Ashkenazic and Sephardic) have it that way, as do the influential siddurim of R. Hirtz, Shaloh, R. Zalman Hanau and R. Yaakov Emden.
So far, the earliest siddur I've found that has במדת הרחמים is that of R. Shneur Zalman of Liadi. I haven't come across anything giving a reason for this, though, nor whether it was his innovation or if he had an earlier source for it. (The various other recensions of the Ari's siddur have רחמים.) Could be that it's for the sake of consistency with various other places in davening where we refer to מדת הרחמים, such as in the preamble to the Akeidah and in the piyut מדת הרחמים עלינו התגלגלי; at any rate, that seems a possible reason why this version has infiltrated into other nuschaos.