As I read through the comments posted above I have to ask myself which game called "Oblivion" everyone has been playing. My confusion stems from the following:
According to any bit of information I have ever read or witnessed through game play in Oblivion, the two sets of armor have quite a few distinct differences. I will warn everyone, however, that the following will contain quite a bit of math; albeit, not extravagant or wildly complex math. Essentially, anyone with a working knowledge of algebra, ratios, and percentages would hardly find themselves pressed to comprehend. I digress. First, let us establish a few base averages. Upon perusing the UESPWiki, one finds the following values:
As a legend I will establish the following units of measure in the absence of tangible ones dictated by Bethesda. Let...
L = light armor
H = heavy armor
W = weight
D = durability, which is equivalent to the amount of damage the item can receive before it becomes broken (think of it terms of Health/hit-points)
P = protection
Light armor has an average weight of 25.37857143 (which will be further shortened to 25.38W) units of measure; additionally, we find that it has an average durability of 1919.142857 (shortened to 1919.14D); furthermore, it offers an average level of protection of 30.96428571 (or 30.96P).
Heavy armor has an average weight of 111.5357143 (or 111.54W); it has an average durability rating of 4349.285714 (or 4349.29D); and an average protection level of 51.07142857 (or 51.07P).
The next step is to take these resulting values and turn them into a set percentages where light armor values are compared to heavy armor values on a scale of 100. The formula is as follows: LX(100)/HX . Where X = the appropriate attribute (W, D, or P). Stick with me...
LW(100)/HW=% or 25.38(100)/111.54=22.75%
LD(100)/HD=% or 1919.14(100)/4349.29=44.13%
LP(100)/HP=% or 30.96(100)/51.07=60.63%
By examining this data we find some very interesting facts about the most basic differences between the two different armor types. Firstly, that a full set of light armor on average only weighs about 22.75% of what its comparable heavy armor set weighs. Secondly, that light armor is only 44.13% as durable as heavy armor; which means that you'll have to repair it more than twice as often. Lastly, we find that light armors offer an average of 60.63% of the level of protection that its heavier counterparts offer. These are all important factors to consider when deciding which is best for your use; additionally these numbers become even more complicated when factoring in the--for lack of a better word--perks that are gained at each skill-level (Novice, Apprentice, Journeyman, Expert, and Master). Take, for example, the following data:
The Light Armor skill-set obtains the following perks in the order respective to their skill-level (0 to 100): 150% decay rate, normal decay rate, 50% slower decay rate, zero encumberance when worn, and 150% protection rating. This data can be interpreted based on the above listed values, or...
From 0 to 24: W=25.38, D=959.57, P=30.96
25 to 49: W=25.38, D=1919.14, P=30.96
50 to 74: W=25.38, D=2878.71, P=30.96
75 to 99: W=0, D=2878.71, P=30.96
100: W=0, D=2878.71, P=46.44
The Heavy Armor skill-set obtains the following perks in the same order, respectively: 150% decay rate, normal decay rate, 50% slower decay rate, 50% encumberance, and zero encumberance. Therefore, we can obtain the following values...
From 0 to 24: W=111.54, D=2174.65, P=51.07
25 to 49: W=111.54, D=4349.29, P=51.07
50 to 74: W=111.54, D=6523.94, P=51.07
75 to 99: W=55.77, D=6523.94, P=51.07
100: W=0, D=6523.94, P=51.07
Bear in mind that zero ENCUMBERANCE is NOT the same as zero WEIGHT. It merely means that the item(s), as WORN, will affect the player-character's movement and attack speeds as though the item(s) weighed nothing; but they will, in your inventory continue to weigh the same as they normally do, irrespective of your skill-level. Had to throw that in there to clear up a possible point of confusion. Now, to more math! From the above results we can determine the following:
At the lowest possible skill-level (between 0 and 24) the percentages listed above remain the same; however, at the highest possible skill-level (100) we find an interesting bit of information. As both armor types result ultimately in zero encumberance, it can be inferred that both types are equal weight-specific when worn. In terms of durability we find that light armor continues to decay at roughly the same rate--by comparison to heavy armor--as it did before with a meager increase of only 0.00006763% (a value which is nothing to write home about!). Most importantly, we find that at a skill-level of 100 light armor only offers 90.93% of the level of protection that heavy armor does. In short, the end result is that both armor types will encumber you the same, but you'll be able to carry a considerably larger amount of additional equipment if your opt for light; additionally, you will continue to repair your light armor at slightly greater than twice the rate of heavy armor; finally, you won't get quite the same protection from light as heavy, but 90% is close enough to be negligible.
My--thoroughly explained--conclusion is that starting out one will notice a vast difference between the two armor types based on your player-character's respective skill-levels, however, as you increase said skill-levels the spread of variation begins to narrow and it really becomes a matter of the type of character you are playing. These numbers combined with an extensive knowledge of the leveling system and how each skill-set is governed by your attributes and their parent skill-groups (Combat, Magic, and Stealth) make for a very potent character. As each armor type (and particular skill-set) is governed by a separate skill-group it is easier for a person whose class is Combat-based to level each skill-set inside that entire skill-group and therefore the appropriate skill-set for his armor type. The end result is typically one in which the type of armor you wear is the one suited to your particular style and tastes. But, as with most RPGs the bulk of the game doesn't lie in you maxing out your skills. The VAST majority of your time in Oblivion was spent getting those skills to their uttermost limits.