How would you finger, say, this chord ? Granted, it says how to finger it, but does anyone do it a bit differently?

Its just that...when moving up and down the fretboard in the same formation, especially quickly, I have a complicated time getting back into position at the new fret (even though it really shouldn'tve changed at all). I suspect it may be a pinky strength problem, or at least a pinky independence problem, though I don't really have any pinky problems in other regards.

So I figured I'd get some input from you folks.
I almost always bar with my pinky, or just NOT play the octave. You don't hear the difference anyway when you play stuff like me :p

Sometimes I play it like that though (the picture), but only when I have to shift notes up or down independently.
you need to use your pointer finger (1), your ring finger (3), and your pinky (4). you also don't even need to use the pinky for this chord, but it adds a little bit more power to it...that's why it's called a power chord!

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I finger it the way it is in the diagram, though sometimes people barre the higher two notes with their ring finger. Though I wouldn't recommend that - it adds tension having to drag that barre around.

Just try to relax as much as you can when changing positions. Try this to get the movement down. Don't worry about your 3rd and 4th fingers for a moment. Just reach up and lightly grab the neck, with your index finger on the root note, and your thumb directly behind it on the back of the neck. Focus on that formation between your thumb and index finger, and practice sliding it up and down the neck to different positions. Don't even worry about picking it yet. Just concentrate on getting the movement right. Once that feels comfortable and natural, add in the 3rd finger, practice some more, then add in the 4th.
I finger it that way, but what you need to remember is that it's the first three notes of a major barre chord. So imagine you were playing a major barre chord on a guitar with just three strings, that's how i learnt to play triads!
Quote by tenfold
The most efficient way to play it would be with the index, ring, and pinky.
Eventually, moving it will become very easy, just takes some hard work.

This is true, but I don't see a problem with playing it with just the first and third fingers. It's only "sloppy" if it sounds sloppy (to answer jfreyvogel's point), and sometimes freeing up your little finger is useful!
I finger it the same way as the diagram. I used to use only my 1st and 3rd fingers, but I found that if I also used my 4th finger I could use it to mute the 3rd string instead of relying on only hitting the top 3 strings. I don't like the sound the chord makes when you accidentally hit the 3rd string - a perfect 4th on top of the power chord.
It helps to learn it with the pinky down, since there are times when you want to mute the 3rd string to only use 2 notes, and it's easily done using the pinky since your hand is already used to that position.
I finger it the way the diagram shows, I also use my index finger to mute other strings (Tip of my finger when muting lower strings and the rest of the finger is resting on the higher strings)
Replace the 4th finger with the 3rd or in other words use the 3rd finger to press the 4th and 5th string.

You can also not play the note on the 4th string. It works as well.
Thanks for the help, guys! Something I have noticed I do is set down my middle finger on the fret above whatever the ring finger is fretting. Might that also be slowing things down? It just seems too awkward to have the middle finger just waggling not fretting anything.