Sorry, but to be pedantic for a second: do they consume more energy, which is really what I care about for battery life? (Let's assume I'm committed to asking the machine to do whatever work it is that I asked it to do, so the required computation is constant, for discussion.) My understanding of AVX is that it consumes more power, yes — but the point the parent makes is a good one: if it finishes faster, where does the energy use come out? More power over less time can mean less energy. (Or more. Depends on the additional power vs. the time saved…)
1. This all depends massively on the actual workload and chip, a lot of people are basically winging it when it comes to AVX power consumption stories. The rub is also that, especially on laptops, you can get convexity in all the scaling problems e.g. you do more work, good, but then the laptop throttles then stays throttled for a while etc.
2. The original (real) power issues with the original/early AVX-512 desktop chips have basically gone away. It's not far off the timescale that you'd looking back to be bashing AMD for bulldozer.
I'd measure it for you on my machine but I don't have an accurate power-o-meter for my computer.