It tends to be pretty chilly for late season grouse in Maine, and when I'm doing a lot of walking, I tend to rest the wrist across my fore arm, with the butt tucked up beneath my arm, right hand across the left ( I'm a southpaw). I never wear a glove on my left (trigger) hand, but do wear a thin deer skin glove on my right hand. A straight gripped gun stands the risk of sliding forward across your fore arm, whereas a pistol gripped gun stays right there.
James Purdey developed a popular trigger bow design for straight gripped gun.
Ironically, it's shape is precisely that of a pistol gripped gun.
Additionally, as arthritis get worse, the added twist to my wrist is a touch more painful.
I had a 32" straight gripped VHE, which I recently sold to another member for that reason. I also have a straight gripped CH, but haven't had it long enough to try it out, but I'm not expecting it to feel any different that the VHE.
Apart from Parkers, I also collect 'Special Order' Winchester 1894 rifles, with a strong preference towards pistol gripped guns (and half round barrels with set triggers, if we're getting picky)

It is really odd the number of Parker single barrel traps that were built with straight grip stocks. The percentage of straight grip skeet gun stocks compared to pistol grips is even more pronounced than single trap gun stocks.

straight grips
 

I like them both. One item not mentioned so far is the length of pull. A lot of american straight grip guns were made with a 14" length of pull. Too short for a lot of people. European guns were much longer LOP's on straight grip guns. Sure a pad can be added but lot's of shooters look for that "feel" just as the gun sits. If more guns of american manufacture had at least a 14 1/2" pull with a straight stock they would be more acceptable I think.

IMO a small framed gun looks better as a straight grip. A straight grip seems to fit the idea of a small, light bird gun better.

A large frame, let's say #2 or larger, looks better as a PG. I think it would look kinda funny to be shooting ducks with a #6 frame gun with a straight grip.

Aside from looks, I couldn't care less which type it has.

That's probably true up to a certain point, Greg, but have you ever tried to handle one of these diminutive British .410s that were in such abundance (and cheap) years ago? If you have even slightly large mitts, they're like gripping a soda straw. I've handled a 00 frame 28 Parker with a straight stock and it's just a tad too dainty. I feel like I am holding onto my 00 frame PG 28, and it doesn't feel so whippy.

Greg mentioned a #6 frame straight grip gun. I guess it's time to go shopping.

I have a DHE with 34" barrels and a straight grip. Being a person of smaller stature and hands, I feel that I get a better grip with this stock and therefore handle the longer length. As Mr. Phillips stated the length of pull on my gun also suits my stature.

I'm drawn to small bore and straight grip guns like a moth to the light. I hunt and shoot targets primarily with straight grip guns. To me they look better, handle faster. Sometimes they are a little thin in the wrist but it doesn't cause a problem. I'm NOT a 12ga guy but one of my favorite target guns is a BHE 12 straight grip on a #2 frame. 30 inch Damascus barrels choked full and fuller. The other one is a grade 3 top lever hammer gun #2 frame and a straight grip.