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First, the skill cap. Formula is "maxSkill = capapilityLvl * stat".
For example a capability V leader with 50 intelligence can get ints intelligence skills to 250 max. A capapility I leader with 20 intelligence will never make it past skill level 20.
Second, the experience point gain (and possibly alos the success rate iin conversing xp into skill points). I don't have the math for that. I just know from experience that a CAP I governor with zero starting skill can be in office for 20 years and still have his skills in the one-digit or low two-digit range, while a CAP V leader after the same time has developed skill levels well above 50. My capital, where all the big industrial assets are, always gets at least a loyal cap IV governor.
Don't discard the low CAP leaders entirely. Sometimes you roll a CAP II with one very well developed skill, like a technician skill of 70 or such. He won't grow very much anymore, but even a CAP V would take many turns to get where he already is. Such leaders are useful, espacially in the early game when administrative resources are scarce.
The xp impact is correct. Capability directly alters the xp gain, the exact numbers are in the manual. Cap 2 gets 30% more xp than cap 1 for exemple.
High capability tends to be better as they tend to have higher int/cha/war so they have higher skill caps and get there faster. Due to the randomness however some low cap leaders can roll high stat levels which can make them good if you have ways to make their earn lots of xp quickly (OHQ, secret service or cabinet member with cabinet retreats).
I suspect that capability level also makes it so that the skill gain is slower with a similar amount of xp but it's hard to confirm as the mechanic isn't documented (the one in the manual seems to be wrong).