The 1837 edition omitted the phrase “even as with the power and authority”, probably because the typesetter’s eye skipped from the first instance of power and authority to the second one. It is also possible that the omission was intentional (especially given the near redundancy of the omitted phrase). Yet the deletion was not marked in 𝓟 by Joseph Smith in his editing for the 1837 edition, nor does the resulting “they taught with power and authority of God” sound quite right without the original definite article preceding power. In fact, the 1874 RLDS edition made that very change in the text (that is, it supplied the the before power). There are two other occurrences of “power and authority of God” in the text, and both of these have the definite article before power:
Of course, the original text here in Alma 17:3 did have the before power, but only before the second power (the one followed by the modifying prepositional phrase “of God”). If the original 1837 change were really due to conscious editing, one would think that the definite article before power in “the power and authority of God” would have been retained.
In the 1908 RLDS edition, the missing phrase (“even as with the power and authority”) was restored to the text, and the intrusive the before the first power (the extra the introduced in the 1874 RLDS edition) was removed from the RLDS text. The LDS text, on the other hand, has retained the 1837 reading.
One possible reason for consciously omitting the phrase “even as with the power and authority” is the occurrence of the as. In current English, the as implies a hypothetical aspect, as if the text is saying “even as if with the power and authority of God”. Clearly, the sons of Mosiah taught with the power and authority of God. The purpose of the as is to indicate that by all appearances their power and authority was from God. Interestingly, there is an example in the text of as if with that also has little, if any, hypothetical sense:
The meaning of “they had fought as if with the strength of God” seems to be ‘they fought by all appearances with the strength of God’. The critical text will therefore restore the original reading in Alma 17:3 (“even as with the power and authority of God”). Despite the unexpectedness of the as in Alma 17:3, its original use here appears to be intentional.
Summary: Restore in Alma 17:3 the phrase “even as with the power and authority”, thus maintaining the earliest reading: “and when they taught / they taught with power and authority even as with the power and authority of God”; the use of as in the final phrase appears to mean ‘by all appearances’.