This question is actually very interesting because of the fact that it makes me think about a construction I do not use often in writing Latin.
We can start from a note from the O. Riemann Latin Syntax, 7th edition, Paris 1927, page 122 §55 note 1. "In the archaic times we find memini and obliviscor with the accusative and the genitive”. During the classic time personal pronouns and reflexive pronouns are always in genitive case. During the classic time personal nouns in the genitive case with memini is rare and familiar. In the imperial time the construction of personal nouns is the regular syntax. For thing nouns the accusative case lasts for more time but the genitive case strikes it during the imperial time. If memini means “mention” it is constructed with the genitive case (Caes. De bello civili 3, 108, 2 “eundem Achillam cuius supra meminimus”).
And then from an other normative syntax, the Ernout et Thomas, Syntaxe Latine, Paris 1964. Ernout&Thomas is more precise, on page 52 §65:
An old alternation existed with the accusative. In the Latin using the genitive seems to have an idea of effort in remembering; rather the accusative indicates something one remembers clearly and is more frequent with things. Cic. Fi. 5, 3 “vivorum memini” Pl. Mi. 1378 “officium memini”. With a neuter pronoun like “aliquid” or “multa” the accusative is the rule because of the possible confusion with the genitive (alicuius or multorum).
So according to this two passages we can conclude that there is no substantial difference of meaning between the two constructions, especially in the classical and imperial time, but only a more common use, the construction with a genitive case.
I hope that this answer will satisfy your curiosity.
