I'm hardly an expert on this, but I think you need to draw a distinction between what you're actually talking about here. "Fresher" can mean different things. Are you talking about feeling dry, or feeling cool because the two are not the same.
The way the human body works is that sweat is created to conduct heat away from the body. The longer the sweat remains on the skin, the more heat we lose. Feeling clammy may not be enjoyable, but it should be a good way to lose bodyheat.
I can believe that oxford vs poplin of equal weights will mean the oxford will make you feel drier due to the openness of the weave and the effect of this on air permeability, but the drier you are the less heat you lose. And poplin clings to the skin when you're sweaty? Great, that means the insulating layer of air you had between your skin and your shirt is now gone, and the heat can pass right through the conductive moisture from your skin to the outside of the shirt. This is the opposite of feeling fresh in my book, but it'll feel cooler because it's literally a more efficient way to move heat out and away from your body.
There's a reason why the government where I live makes announcements almost every winter urging people not to wear cotton. Wool dries easily and leads the moisture away from your body so you stay dry and warm, cotton gets wet and stays wet for hours and hours, acting as a heat conductor leading bodywarmth away from your body, people die from this every year.
And of course there's the fact that poplin tends to be lighter weight than oxford. I don't know if this is a necessity, but it's what I've found to be the case, so if I want to put on my thinnest and lightest shirt, that'd be a poplin shirt, and if I was going to wear an oxford shirt instead, the thinnest oxford I have would be considerably thicker than the thinnest poplin. So in terms of both heat and moisture transport, that should be a bad thing. For two weaves of equal weight, obviously a more open structure is an advantage, but if the open structured weave tends to be heavier than the tighter weave, it becomes a balancing game of which effect dominates. Oxford has a more open weave I'm sure, but when the "tight" poplin is so thin I can easily see through it, my suspicion is that quite a bit of air gets through it as well. My experience is certainly that wearing just a thin poplin shirt in the wind is a lot breezier than wearing a thicker oxford shirt.