There is no firm evidence whether IPv6 has net energy consumption greater or less than IPv4 for the same application layer traffic load. There are factors that might work in favour of IPv6, such as a larger minimum PDU size or less energy spent on network address translation, and factors that might work against it, such as the transmission time for longer packet headers or greater use of link-local multicast. Equally, there is no evidence whether different co-existence strategies (e.g., native dual stack versus IPv4-as-a-service) have significantly different energy costs.
BCP 202 makes specific recommendations on reducing the energy consumption of IPv6 Router Advertisements.
It is worth noting that in the area of constrained IPv6 nodes with very limited battery power and transmission capacity [RFC8376], considerable attention has been paid to energy consumption, including compression mechanisms such as Generic Framework for Static Context Header Compression and Fragmentation (SCHC) [RFC8724].