I don't think there is necessarily a difference in the volume absorbed, but my experience with silk and polyester scarfs is that the polyester will dry faster, which isn't what you want if you're after evaporative cooling. When dry, the silk feels more breathable and less stuffy (but this will come down to the weave of the polyester you're comparing it against). The silk also tends to have a bit more body, which equates to coverage when you're using it for sunblock. The feel of silk against skin is super luxurious -- which isn't to say that polyester is uncomfortable, but it just can't compare to a high quality silk.

In this application, the only advantage polyester has is that it is cheaper to produce.

I also occasionally get complements on my scarf when stopping at bakeries or cafes. And they're right, I do look good, but inside it always makes me laugh when I get sartorial complements on tour. If they only knew how long it's been since I last showered or did laundry...