A modern CPU should be able to decode 1080p in software without breaking a sweat. I had hardware decoding disabled in Firefox until recently and the difference is unnoticeable to me.
I don't usually use hardware decoders because there are restrictions, such as what renderers can be used or what and where filters can be placed in the decoding and rendering pipeline.
Hardware decoding is great when power (be it electrical or processing) is limited, but if you really want to have all the knobs available software decoding is what you want.
Regarding battery life, I really haven't noticed a difference on a 6800U. Both hover around a disappointing 7W.
Not true for modern codecs such as AV1