There are two basic approaches to understanding the discrepancies between Yitro's proposal and Moshe's implementation. The first approach views the differences as meaningful, while the second minimizes their significance. Each of these main positions can then be further subdivided:
A Significant Omission
The omission of "God fearing, men of truth, who hate unjust gain" (יִרְאֵי אֱ-לֹהִים אַנְשֵׁי אֱמֶת שֹׂנְאֵי בָצַע) in Moshe's implementation is significant. There are two somewhat similar variations of this possibility:
Not Extant
Moshe could not find people who had all of the desired qualifications in Yitro's job description so he was forced to settle for those who were merely "capable men" (אַנְשֵׁי חַיִל).
Number of judges – See Yitro's System that according to Rabbinic sources and Rashi, Moshe needed to appoint 78,600 judges. This would explain his need to settle for lesser standards.3
Relationship to Devarim 1 – Sifre Devarim, Devarim Rabbah, and Rashi all agree that Shemot 18 and Devarim 1 are two accounts of the same event. In addition, Sifre Devarim and Rashi explain that the criterion of "men of understanding" is missing in the selection in Devarim 1:15 because it too could not be found.
Only Hashem Knows
Of the four criteria Yitro mentioned, only "capable men" (אַנְשֵׁי חַיִל) can be readily ascertained by human observation. The other three characteristics are all matters relating to the person's inner soul, which only Hashem can know for sure.4
"אַנְשֵׁי חַיִל" – Ibn Ezra interprets this as men possessing endurance and courage.
Relationship to Devarim 1 – Ibn Ezra assumes that Shemot 18 and Devarim 1 are two accounts of the same event, and he explains that the qualities mentioned in Devarim 1:15 are also externally verifiable.
Not a Fundamental Change
The omission of "God fearing, men of truth, who hate unjust gain" (יִרְאֵי אֱ-לֹהִים אַנְשֵׁי אֱמֶת שֹׂנְאֵי בָצַע) in Moshe's implementation is not a fundamental change. This position also subdivides into two closely related variations:
Included Under the General Term
"Capable leaders" (אַנְשֵׁי חַיִל) is a general term which incorporates all of the other traits (כלל ופרט).
"אַנְשֵׁי חַיִל" – Since according to Ramban this is a general term, it cannot refer to a specific qualification such as strength, wealth, or military prowess. Thus, Ramban interprets it as describing people capable of leading a large group. See חַיִל for further discussion of Ramban's position. Cassuto, on the other hand, explains that it refers to a person possessing many good attributes.
Additional variations – Cassuto suggests that all of the differences between the descriptions of Yitro's advice and Moshe's implementation are merely the products of standard literary variation when repeating information.6
Relationship to Devarim 1 – Ramban maintains that Shemot 18 and Devarim 1 are two accounts of the same event, and that the term אַנְשֵׁי חַיִל includes also the traits mentioned in Devarim 1:13-15. In similar fashion, Ramban Devarim 1:12-13 interprets וִידֻעִים as a general term which subsumes all of the necessary judicial qualifications.7
No Need to State the Obvious
The entire nation possessed the traits of being "God fearing, men of truth, who hate unjust gain" (יִרְאֵי אֱ-לֹהִים אַנְשֵׁי אֱמֶת שֹׂנְאֵי בָצַע), and thus it was unnecessary to specify them in Moshe's implementation.
"אַנְשֵׁי חַיִל" – Abarbanel interprets this term as military commanders.
Relationship to Devarim 1 – Abarbanel maintains that Shemot 18 and Devarim 1 are two accounts of the same event, but that Moshe needed to add qualifications to Yitro's list, as Yitro did not have a correct understanding of how the judicial system was supposed to work – see Did Moshe Need Yitro's Advice.