tx, PC.
Re skills: Look at it this way: The 20th level wizard is not, in fact, stronger than the 1st level fighter (well, clearly not). But he's capable of dealing with athletic challenges that give the 1st level fighter trouble. Why? Well, maybe because he's using magic to deal with those challenges -- that's just flavor; the important thing is that when he needs to, say, climb a tree or jump a 5 foot crevasse, that he has a way of reliably doing so--the fact that he's using magic to do so (in your universe, anyway) is just flavor, not mechanics.
Note, btw, that the same wizard is -not- capable of avoiding damage from a height -- because unlike climbing or jumping (which anyone can do), using acrobatics to avoid falling damage requires that you be trained! Similarly, a 20th level Barbarian knows a bit about magic and can make some guesses -- just look at Conan! But he can't detect magic -- because that's something you actually have to be a mage (eg, be trained at) to do!