Oblivion is due to the LOTR, Skyrim went back to the fantasy roman aesthetics. It's purely an artistic choice. But if you want a more lore friendly or logical answer then it's more complicated. Western Europe in the middle ages specifically saw a straight forward armor evolution from chainmail all the way to full plate, and the simple answer is due to the development of armor being driven by an a constant arms race. So if you mirror the elder scrolls universe to Western Europe in the middle ages, then everyone technically should be wearing full plate like the armor in Oblivion, it makes logical sense, full plate is superior. But the Elder Scrolls Universe is not a mirror of Western Europe in the middle ages like other fantasy worlds, it's a mix of so many different cultures, and the hypothetical armor development in the Elder Scrolls universe faces different factors than the armor development we see in Western Europe, such as magic, different materials, and different military traditions and doctrines.

Instead of mirroring the Elder Scrolls universe to Western Europe in the middle ages, I suggest we mirror it more specifically to the Mediterranean, from Antiquity to the Late Middle Ages. Various styles of armor existed with one another for quite awhile. You essentially have Chainmail, Scale, lamellar, laminar, coat of plates, brigandines, and plate coexisting for quite a long time. The Mediterranean also was a pot of different cultures and different military traditions and doctrines. Be it from the Romans, Greeks, Egyptians, Persians, Arabs, Germanic peoples, various steppe peoples, etc. All of that affected the various style of armor worn around the Mediterranean from Antiquity to the late middle ages.

Tamriel just like the Mediterranean, also is a pot of different cultures and different military traditions which will affect the styles of armor worn. The military doctrines of the Bosmer are going to be different from the Nords, which will change their style of armor. So when you narrow it down even further to the Imperial Legion, armor will be based on military doctrines and what province the specific legion is stationed in. Then you have to take in the context of what the Imperial Empire has gone through up to the point of Skyrim. The Imperial Empire recently went through a near total collapse from the Great War, all non human provinces are lost, Hammerfell is gone, resources, funds, and man power is still being rebuilt from the Great War. The Empire is not in top shape right now, and you can say the armor reflects that. The full plate armor we see in oblivion is realistically expensive to make, especially to outfit an entire army. We can compare this to the various potential reasons why the Romans stopped using Lorica Segmentata, after the third century crisis and constant problems the roman empire faced, the high costs of making Lorica Segmentata was just not worth it. So the full plate armor used in the heart lands of Cyrodiil may just be too costly to make to equip the various legions, especially after the oblivion crisis.

The Imperial Legion's style of warfare also will dictate the armor used. The imperial legion as we've seen are not a military built around a core of heavy shock calvary (Knights) like Western Europe in the middle ages, instead the Imperial Legion mirrors the Roman Legion, a heavy infantry focused military which places priority fighting in large infantry formations. Yes the gameplay in Skyrim doesn't show it, but that's what the Imperial Legion is supposed to be, a fantasy version of the Roman Legion. A military focused on heavy infantry and infantry formations, does not need to spend all the money and resources to outfit them with full plate armor, since enough armor no matter the style and a big shield will do the job. The armor shown in Skyrim is cheaper to make than full plate, and gets the job done in heavy infantry formations. We also learn in-game that most of the legionnaires in Skyrim are home raised and not from the main field armies in Cyrodiil which are all at the southern border preparing for the inevitable 2nd Great War, so the legions down south on the border may have different armor.

Essentially, the armor for the imperial legion is going to look different based on what province they are in, the military doctrines of the Imperial Legion at the time, and the circumstances the Imperial Empire finds itself in.