Sometimes annexation draws attention to the first term (muḍāf); at other times the discourse uses the relationship to stress the importance of the annexed term (muḍāf ilayh). The source discusses alternative analyses here rather than a single automatic result.
«عَبْدِي حَضَرَ» may emphasize a person through the speaker's own association; «عَبْدُ الْخَلِيفَةِ رَكِبَ» can raise the servant's perceived status by association with the caliph.
The grammatical relationship itself does not determine the full rhetorical effect. Context, intention, and the hearer's valuation identify which party is emphasized and in what way.