As with a lot of armoring questions looking for "the" way things were done, I suspect it's both...and more. The King's Mirror of c. 1250 says to wear the plates (from nipple to navel) under the hauberk. (Explains why references to coats of plate appear in the 13th century more frequently than depictions.) Before around 1330, I'd say wearing an over-coat (surcote) over them was most common, with the period until the 1350s showing both options. After that exposed plates without a gypon or surcoat seems to be more fashionable. By the 1370s you start seeing the big sleeved coats covering everything except the bascinet/aventail and gauntlets, but CoPs were on their way to being replaced with more solid breastplates by then.
ferrum ferro acuitur et homo exacuit faciem amici sui
By 1380 I doubt any knight would not be wearing some form of rigid or semi-rigid armour over the torso. Once you get into the 1320s it is very unusual for knightly equipment to lack such armour, by 1380 for most of Europe I'd guess it just did not happen as Plates were dirt cheap. I suppose the question could still stand as how do we know he was not depicted in this effigy w/out such armour but he himself I'd say unlikely.
My guess is that he is wearing it under in the first and without in the second. A quick answer is that dags do not a Pair of Plates make but I tend to look for drawn edges of plates and/or rivets.
Jumping slightly off topic, I think the 1380 date on Huglin is a bit later than it should be.
The effigies and brasses site lists 1369 while the THEMCS page gives 1362 for the effigy and 1377-86 for his death. I couldn't find any better dates, but in general it suggests the use of mail mittens at a pretty late date along with his leg defenses.
Sean Powell wrote:Question: What makes you think the first statue is wearing a CoP rather then just maile and a tabard?
Sean
I could pull out a few others when I get home, the notable thing on them I'm trying to point out is that when the dags are on the shoulders, there does not seem to be the rivet/plate line on the body - and with the art depicting rivet/plate lines, there does not seem to be dags on the shoulders.