While copying from 𝓞 to 𝓟, Oliver Cowdery accidentally replaced the determiner that with the. The 1981 LDS edition restored the that. Since the great and abominable church has already been referred to many times, either determiner will work. In all, there are 12 occurrences of “great and abominable church”, and in the earliest textual sources we have eight occurrences of that, two of the, and two of this. In one of these cases, the that was replaced by a, again by Oliver Cowdery when he copied from 𝓞 into 𝓟 (see 1 Nephi 13:26).
Summary: Based on the earliest textual source (the original manuscript), the original determiner in 1 Nephi 14:15 should be maintained (“that great and abominable church”).