Strange sink behavior -- sink fills partially then drains at a normal pace
My first thought was venting as well.  The washer and tub may have different vents and have no bearing.  I'm assuming, of course, that you tried the simple approaches, like pulling out the drain stop to ensure it isn't clogged with hair and gunk, and dropping the trap to ensure it is clean?  I had an issue like this with a tub drain where the vent was clogged, and there was no way to get to it. I worked at it with a hand snake and plunger for a while and it eventuially opened the clog.