Grading: (1) This report is "sahih", and there is no harm in its men (narrators).
Technical note / Defect ('illah): The "mahfuz" (preserved) form in the narration of Ahmad bin 'Abd al-Jabbar al-'Utaridi is that he narrates this story from Yunus bin Bukayr, from Ibn Ishaq, from Salih bin Ibrahim, from his father.
Details of the narration: The narrator said: We were travelling with 'Uthman bin 'Affan (may Allah be pleased with him) on the road to Makkah when he saw 'Abd al-Rahman bin 'Awf (may Allah be pleased with him), and 'Uthman (may Allah be pleased with him) said: "No one can claim to surpass this elder (shaykh) in merit in both emigrations." He meant the emigration to Abyssinia and the emigration to Madinah.
Reference / Source: Ridwan bin Ahmad al-Saydalani likewise narrated it from Ahmad bin 'Abd al-Jabbar al-'Utaridi, as found in Ibn 'Asakir's "Tarikh Dimashq" (35/ 253).

Technical note / Defect ('illah): As for the narration of al-Miswar bin Makhramah, it was Humayd bin 'Abd al-Rahman bin 'Awf who received it from him.
Reference / Source: Ibn Sa'd (3/ 116), Ahmad in "Fada'il al-Sahabah" (1251), al-Tahawi in "Mushkil al-Athar" (3565) and Ibn 'Asakir (35/ 253).
Details of the narration: This narration is by way of 'Abdullah bin Ja'far al-Makhrami, from 'Abd al-Rahman bin Humayd bin 'Abd al-Rahman bin 'Awf, from his father, from al-Miswar.
Grading: This chain is "sahih", and this is the "mahfuz" (preserved) form in the narration of al-Miswar.
Important point: In this narration the wording is: "Whoever claims that he is better than your maternal uncle ('Abd al-Rahman bin 'Awf) in the first emigration and in the later emigration has lied." Here the mention of "the later emigration" is an addition.
Note / Clarification: It appears that Ibrahim bin 'Abd al-Rahman bin 'Awf and al-Miswar bin Makhramah were both present in that caravan, and both heard 'Uthman (may Allah be pleased with him) say this. And Allah knows best.