There can be lots to possibly consider, but something like extensions really don't lie at the heart of 'big, juicy chord voicings'. What you'll ultimately want to look at are these, in no particular order:
>Timbre & expression:
Timbre is a very big consideration: you can get a big, thick sound with only two or three notes as long as the timbre is rich enough. Expression can help augment the timbre's qualities, too: a louder piano stab is going to such more much big than an incredibly quiet push into the keys. v
Very quiet, soft flutes playing what should be a 'dense' voicing aren't going to sound particularly juicy or impactful, either.
>How the frequency spectrum is filled: the voicing isn't going to sound very 'big' and & 'juicy' if all the voices are at, say, an extremely high register. You're generally going to spread your voices relatively far across the frequency region (at least, relative to the extreme high register voicing I theorized above). Though note this: the basis for the 'meat' of a big sound is going to be found in the middle register of human hearing; you generally can't have a big, juicy sound from merely an extremely low-pitched or extremely high-pitched sound, or even both played together concurrently. It needs to be based moreso in the middle register; the frequency extremes only serve to augment the middle register basis (if the extremes are used at all in your particular voicing) in context of 'big, juicy voicings'.
>The intervallic relationship between the voices: you generally won't want just all octaves & unisons playing (unless you have a timbre absolutely chock-full of rich overtones, which can fill out the sound in a quasi-harmonic, pleasing way.
A power chord played by a distorted guitar is a great example; even though it's played as a perfect fifth, which is often thought to be very bare with a pure timbre, the overtones created by the distortion are so strong & present that the overall power chord sound is incredibly thick & full. You likely won't want minor second clusters in most cases either, though they can definitely work if you contextualize them properly. Overall, think about the intervallic relationships too, and if they're inherently rich. They don't have to be extensions by any means; listen to traditional jazz bands or baroque music groups for incredibly full, triad-based music that use extensions relatively rarely.
>The number of voices: if you have simpler timbres, you'll generally need more & more voices to adequately fill out the spectrum; manifest the more colorful interval relationships to help, too. Again, there's less of a need to do this with more overtone-rich timbres.
>Context in the larger piece: if you have a lot of chords with meek voicings that start out a piece, with a suddenly big fat voicing coinciding with the climax, this new fat voicing is going to sound all the more rich compared to what came before it. It makes it seem all the more bigger as a result, since everything before was so small by contrast.
There's a lot more that I could go over, but take this lesson away from it: lots of aspects (timbre, expression/loudness-intensity, register, intervallic relationships, musical form, wider context of the piece, and more) are all equally-valid domains that you need to think about chord voicings from. They're all dependent on each other, and shape the ultimate end result. People aren't taught about these dimensions in school much, so they're often-skipped over in analysis & when talking about music, but they're by-far the most important in this context.
I hope this was helpful!