Why does one of my bathroom sinks drain slowly when the water is running, but drains quickly when filled and drained?
Warning, wild speculation ahead, but I have had this problem.

I've always thought that the aerated water causes some kind of "bubble dam" that plays with the way the water is able to go through the relatively thin space that the popup creates.  Blocking the bubbles with my hand and letting pure water start going down the drain seems to stop the bubble phenomenon and water will drain faster.

I think removing the bubbles and starting a good flow lets a siphon effect take over and suck the rest of the water down quickly.  The bubbly water never lets a large enough volume of water to drain to start a good siphon.

I have had luck with raising the pop-up drain to allow a bigger gap for water to drain.  Of course, I have also completely removed the pop-up as well because I never need to stop up the drain.