If you're looking for differences regarding actual stats, you wont find it, not in Oblivion at least. In Oblivion, if you had 100 skill in Light Armor, and had the best suit of Light Armor on, your defense rating was 85. Same with Heavy Armor and the best suit of it. So what was the difference, stat wise? Absolutely nothing.
The difference, is immersion, RP, and imagination. Does your character use light or heavy armor? That's the difference. Roleplay. Immersion. Use your imaginations and things start to find purpose.
The difference you say? It's quite simple, really. Although it seems to be overlooked a lot in this thread. Anyhow, at the high-end of the scale, yes, a full set of Daedric armor and a full set of Glass armor provide the same armor resistance. However, Heavy Armor has more health. What does this mean? It means that it takes longer for it to break. What does that mean? It means that it takes longer for it to lose it's armor resistance effectiveness, as once armor deteriorates to 0 percent health, it provides no protection. (It slowly loses protection as it breaks is what I was getting at.)
Furthermore, Heavy Armor had the advantage that it could be mixed and matched while still retaining all of it's perk advantages. That's something which Light Armor does not do. If you mixed and matched Light Armor with Heavy Armor, then you would lose out on the 50 percent extra protection perk that Light Armor provides. To top it all off, there's one key item that comes to mind that's exclusively Heavy Armor (Escutcheon of Chorrol), which makes the factor of losing the 50 percent extra protection perk very important.
Stat wise, Heavy Armor is the clear winner at the higher end of the scale. I imagine that Skyrim will try to make the Heavy Armor and Light Armor skills different, from beginning to end, this time around.