The ‘new school’ ones are default with rigify.
Technically it looks cleaner (well with my rigify code edits to remove the stupidly large arrow widget that covers the whole limb)
But you actually have to do more work because you have to rotate the limb with each move.
The ‘old school’ pole vectors can be parented to the foot and often you don’t need to touch them because they stay aligned with the end control (which is what you want most of the time)
Why are they popular – I ‘think’ it’s because someone made it the default in rigify and most people just go with default, so that’s what they learn.
In my opinion, pole vectors look uglier but they are far superior because you can animate faster.
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