The best system that springs to mind is the Shadowrun (PnP) skill web system. It actually went 3 tiers deep with General Skill / Concentration / Specialization. In that system, increasing General Skills cost more because everything under that skill benefited from the skill level increase. Concentrating in a group up sub-skills costed fewer points since to increase since that level up only affected some sub-actions, but not all. Specializing costed even less than a skill concentration since it raised only one action directly related to a specific weapon or action.
So it often happened that a Firearms skill would be at 4, Pistols skill would be at 6, and Baretta 9mm skill would be at 8.
In that case, to raise the skill levels, you would have to spend:
8 points to raise Firearms from 4 to 5 (2 x current level)
9 points to raise Pistols from 6 to 7 (1.5 x current level)
or 8 points to raise the Baretta 9mm from 8 to 9. (1 x current level)
(Each line is paid for and advanced independently after character creation.)
Consider that if you pick a favorite weapon, you can get deadly with it fast without being completely useless with everything else.
Or if you knew that your favorite weapon won't be available for a while, or would rather remain versatile, you can stay generalized, but less effective than a specialist.
So to summarize my answer to your question:
You should get more rapid advancement by specializing over the versatility of generalizing but at the added cost of being less diverse.