Strength, by far. Bag slots might be convenient and less number-crunchy, but it makes absolutely no sense why a ring takes up just as much space in my bags as a two handed sword or a horse (yes, horses fit in bags in WoW)
That depends on how the system is done, though, in some games, every item takes up one square, but a more logical approach is to have different items take up different amounts of space, a ring might take up only one square, for example, while a larger item might take up multiple squares, of course, this still isn't completely realistic as the space in your bag wouldn't actually be a completely flat space, I also recall when playing Diablo, which used to use this kind of system, why I couldn't turn an item on its side so that it would fit if there isn't enough vertical space for it, but still, it definitely makes more sense than all items taking up the same amount of space.
In the end, though, neither system is completely realistic, because either one leaves out factors that would be important in real life, just because you have enough space in your bag to carry something doesn't mean you'll be able to lift it once it's inside, at the same time, just because you can pick something up doesn't mean there will be enough space in your bag to fit it in. I'd say the most realistic system would be to have both, actually, you have a limited amount of space in your inventory, but you can also carry a certain amount of weight, but in my experience, such a system generally ends up rendering one of the factors irrelevent because you end up reaching the other one first all the time, thus you can effectively ignore the other one because chances are you'll reach the first one sooner anyway, so really, you only actually need one, and out of the two, I think I prefer a weight based system, as it's less restricting, if you have enough weight left for something, you can carry it, you don't need to worry about positioning things in your inventory so there's as much space for large items as possible, thus avoiding some potentially annoying micromanagment, it also allows the amount of items you can carry to be determined by how you play, rather than limited to a static number which you may be able to expand when you get a chance to gain items that increase inventory space.
However, it's been speculated that attributes have been removed from Skyrim, this hasn't been confirmed, though, so whether its relevent or not weights to be seen, if it's true though, I'm not sure how Bethesda would handle the inventory.