The common thread is not the size of the house or the amount of equity in it, but the clock. A homeowner with six months of runway and a homeowner with six days of runway need very different plans even if their properties are worth the same amount.
That urgency is also exactly what a buyer or a lowball offer will try to exploit, since a seller who appears to be in a hurry tends to get tested on price during negotiation.
The right response to a compressed timeline is a fast, honest valuation, not a rushed guess. Get your hand-reviewed valuation from Joel Dyck.