I do not see any difference in meaning between לְמִינוֹ and לְמִינֵהוּ, but the choice of usage between the two may have significance. The word לְמִינֵהוּ closely resembles the hypothetical way of expressing "to its kind" or "to its species" in Proto-Semitic (P.S.). Here, the Tsere vowel underneath the nun indicates that the word מִין ("species", "kind") is in the genitive case. Hence it should be clear that the form לְמִינֵהוּ is archaic and closely resembles what the P.S. would have been. The form לְמִינוֹ is the more typical form we would expect to see according to the grammatical rules of Biblical Hebrew.
An analysis of the frequency of occurrences for לְמִינוֹ and לְמִינֵהוּ is revealing. The word לְמִינוֹ occurs only 4 times in Tanach, with all occurrences being in the Torah. Only once does לְמִינוֹ appear in Genesis 1:11, with the other 3 occurrences being in Leviticus (11:15, 11:22), and Deuteronomy (14:14). The word לְמִינֵהוּ also exclusively appears 14 times in the Torah. However, it appears 8 times in Genesis as well as 6 times elsewhere in the Torah.
I would argue that the book of Genesis has a preference for using the more archaic form לְמִינֵהוּ over the more modern form לְמִינוֹ. In later books (Leviticus and Deuteronomy), both forms occur with a more equal frequency. If we assume that the composition of Genesis and Leviticus are separated by 1000-2000 years, then it is possible that earlier variants of the Hebrew language were preferred in Genesis over the other books of the Torah.