Character attributes and properties, to limit or to distinguish?

When you play your favorite RPG, how different do you feel your character is from other characters of the same class, but with different attributes? Do those attribute difference limit your character or enhance your character? For example is a low intelligence used to limit your spell use or is a high intelligence used to stimulate your spell use? Might sound the same, but it's quite different.

Is the impact of all attributes, regardless of class, important enough that your character feels quite different from one with a two point difference? Are attributes not relevant for the class used to distinguish characters of said class?

I'm concerned that many RPGs don't put enough emphasis on attribute use and end up with characters of the same class which are pretty much all the same. For example a magic user with 18 INT will look pretty much like a magic user with 17 INT and somewhat like a magic user with 16 INT. Simply because the magic user class focuses around intelligence and disregards all other values. So the magic users look pretty similar even when one may have 18 CON and another 13 CON. They both get few hit points, albeit 18 CON gives a bonus. They both get to set off a spell per round. They both have their handy dagger to attack with. So what really tells one character apart from the other?

In the quest for "balance" I find many RPGs tend to put a filter or veil on many attributes which are not directly related to the character class. Thus all members of a class seem the same, or lets say way more similar than their attributes gives them potential to be different from the rest.

Do you take steps in your game to leverage other skills in the character's attributes outside those relevant to their class?