Assuming your game can mimic this power spread, then, your d20 vs d20 mechanic requires that a "high level" character have skill levels at least 10 points higher than a "mid level" character, who must in turn have skill levels at least 10 points higher than a starting character.
This holds true in D&D, but the point spread is a little subjective. In a different setting, say Game of Thrones (low magic, low power), I think those numbers change a bit.
But the starting character is usually a specialist of his kind - a starting warrior should be better at fighting than a starting wizard, say - and thus should probably be significantly higher than zero; probably around +5. So this means that your high level characters have skills of +25, or more likely, +30 and up.
Starting characters in my system vary, regarding this, in three ways: ability scores, skills, and perks. A starting warrior probably has a +1 to fighting from his Physical score, another +1 from his first skill point (in Fight-Melee), and a perk that increases his physical damage capacity, effectively giving him more stamina. He's also likely wearing better armor and weapon than a starting wizard.
Gear aside, that's +2 to his attacking, and probably max damage of 16.
The wizard likely has a low Physical, resulting in a -1. He won't be buying a Fight skill point. He might buy a Parry skill point, but that's not likely. His perk, if he wants to be a casting beast, will relate to metaphysical power, not fighting.
Gear aside, that's -1 to his attacking, and max damage around 8.
So the fighting difference is measurable. However, my system's level 1 is pretty chill: it's for commoners or children, really. Level 2 is a much better measure of specialization. For the high level characters (level 15), especially those who want enough generalization to be survivable, they will probably have 3 good skills (dabble in one or two more), with 7 points each, and then a bonus from ability scores between 3 to 6.
Maybe your game can't mimic this spread. But if not, then why not? It's hardly unrealistic, and it's definitely fun.
The core rules don't mimic this spread. But they can, simply by creating classes, granting more skill points per level, using perks to buy more skill points instead of perks, et cetera. The rules are supposed to encourage modification, and I hope that changing the die of the standard roll and increasing skill points a viable options for that.