How quickly should oil pressure come up?

Let others argue for you:
What Exactly Do The Multi-Visc Designations Mean?

The whole of human knowledge at our fingertips and yet old wives tales persist...

A 10w-40 and a 10w-30 might be the same when cold, they might not (usually not). We'd need a ton more info to know for sure but in most cases the 10w-40 will always be slightly thicker, it'll just have some more or higher grade viscosity improvers to get the hot viscosity higher. But how it's measured cold and how it's measured hot are different and the ranges that qualify for 5/10/15w are pretty wide.

Earlier this year I switched from 5W-40 Valvoline synthetic "Euro Spec" to 10W-40 Penn Grade 1 for my Duster. It picked up 5-10 psi hot oil pressure at idle and above. According to the "ratings" it shouldn't have changed.