Sanctuary of the Crimson Petals is 17%, while another expedition, Shrine of the Deep Blue Heaven is 12.5% -- so nominally worse -- but costs half the supplies.

Math-wise, a roughly 66% chance to score Night Whispers at Crimson takes 6 attempts at a cost of 240 supplies, while a ~66% chance at Blue takes 8 attempts but only 160 supplies. 240 supplies at Blue will get you an ~80% chance.

It's also much easier to avoid spending actions and items avoiding Rivals during a 20 Progress expedition than a 40 Progress one.

The 80% chance at Blue costs 8 attempts at (using Bold) 12 actions per attempt = 96 actions and another (at 1.125 supplies per action, from Underclay sourced SBL) ~140 for supplies. 240 total actions is around 3 busy days worth of candles -- and you may still wind up with no Night Whispers.

OTOH, 240 actions at a not-terrible-for-this-stage-of-the-game 2.3 EPA (Blue has an average pay of 70.1E and 12 A for an expedition + (20 S / 1.125 S/A = 17.78 A) for supplies = 29.78 A, giving 70.1 / 29.78 = 2.35 EPA) gives 550-odd Echoes -- again, on average. That's enough for the Parabola-Linen Suit or Exquisite Ivory Gown or Kingscale Boots you've been eyeing at the Bazaar, anyway, so it's not like the time is being wasted... ;-)

Either way, though, I'd be certain you really need Night Whispers before grinding an expedition to try getting them -- it's RNG locked, so you're never guaranteed to actually get any at this stage. This is unlike peer items such as Crackling Devices (LB Industries), Captivating Ballads (Underclay) and Parabola-Linen Scraps (Tomb of the Silken Thread expedition), which you're basically guaranteed to get after 30-50 actions.