I've not done the larger sized postcards, just the standard size, but I'll tell you what I think of them as a consumer and postal customer.
I judge them based upon the thickness of the card stock and how smooth the face is as to whether or not I give them a second glance. If it feels like quality, then I give them a look. IMO, the tactile sensation is the first barrier to overcome. I think that when you put a post card in the customers hand then you should put a sturdy quality card in their hand, because the post card is an extension of your product.
Even thought the larger post cards "stand out" in the stack of mail, I read them least, if at all.
They can build TOMA if looked at, but I,personally, don't give them much attention.
It makes them seem desperate and I see them as inconvenient and are the first ones I throw out as they take up too much room on the entry table. It makes me think that their business is all hype, "all show and no go", as if they are just a cardboard cut out and not the real McCoy. To me, a sturdy, quality post card = a sturdy, quality business.
If an oversized postcard had a hot topic or a significant one-time event that made me want to call IMMEDIATELY, I'd see them as a stand out value, but the dog eared, bent abominations that I get almost every week are straight into the trash.