Except power attacks are worse than regular attacks for damage over time I'm pretty sure, due to their slower speed. I never use them. Plus I use mostly archery anyway, which doesn't use any stamina unless you zoom but I rarely need to. The only thing I use stamina for is running, really, but the default is always enough, I've never been hurting for stamina.
As for sneaking, I don't go for backstabs, just use arrows. That is a good point though, wasn't sure if heavy vs. light made a significant difference with sneak or not. Seems like heavy armor is ideal for me though. I do prefer the look of light, but just doesn't seem worth it when it doesn't make enough of a difference in mobility.
It really depends on what weapon you are using and how you are perked out.
For example if you are dual wielding swords and you take Dual Savagery, Paralyzing strike and Savage Strike coupled with some of the standards you literly cripple or kill oppoenents outright in a single dual power attack. And the speed of power attacks is actually increased with Dual Fury even though it doesn't state that in the perk description.
You can also use it with other weapons, for example bone breaker and Hack and Slash for axe and mace actually work for power attacks as well.
Your right though strictly speaking you would probobly do more damage with swords, but the power attacks really become almost one shot one kills, and if they don't kill you they are going stagger your opponent.
I haven't experimented with it that much but I find the power attacks as so brutaly deadly its crazy and while stamina is a none issue with a single opponent in those two on one or three on one fights, man that stamina comes in handy because you really need to stagger people and get them off their feet in a single swing else the chance of getting hit more often are a lot higher. I mean the shorter the fight the better for you.
But it needs more experimentation, I can't say Im an authority on the subject, but with dual wielding power attacks I find Im a death machine.