The difference is not apparent in peacetime patrols - the difference can be seen in wartime. Also remember, they are comparing a 86,000 ton CV to a 95000 CVN - not a 60000 ton CV to a 95000 ton CVN.
If you look carefully - you will find the following -
1. The aircraft fuel storage - 1.4 million tons for the CV and 3.5 million ton for the CVN - 2.5 times more - that says something - doesn't it? At wartime that 2.5 times extra means 2.5 times more sorties - which means a CVN is equivalent to 2.5 CVs.
By the way storage in CV was 1.8 million. The excess capacity in Nimitz-class CVN compared to USS Kennedy CV is primarily due to the way CV was designed not because of the propulsion type and also due to the fact that CVN doesn't have to carry the propulsion fuel. You see there is a difference of 7 years between the commission of USS Kennedy (1968) and USS Nimitz (1975) and Nimitz had a better design. And also the displacement of USS Kennedy is 9000 tons less.
A better designed CV will certainly be able to carry more Aviation fuel and may be a fraction less than the CVN provided they have same displacement ton values.
And regarding the aviation fuel, this is what US has observed during Operation Desert Storm - "During Operation Desert Storm, the conventionally powered carriers in the Persian Gulf replenished aviation fuel about every 2.7 to 3 days. The U.S.S. Roosevelt, the only nuclear-powered carrier in the
Desert Storm air campaign also operating in the Persian Gulf, replenished its aviation fuel about every 3.3 days.". Again, here the USS Roosevelt has more tonnage displacement.
2. The carrier range itself - at 28 knots, max range is Singapore to Bahrain (6300 km/ ~4000 miles) - a CV steaming in from Vizag to Vietnam, (2000 miles) will be at the mercy of allies for refueling if it has to sail back home. A CVN can do the same without any problems.
Here is a comparison of a CV and a CVN. There is not much difference in their speeds
And coming to refueling aspect, you have to remember that a CVN or CV doesn't go alone and move as part of a CBG in the sea and they are always accompanied by destroyers and cruisers which are powered conventionally and have limited fuel storage. So they need refueling irrespective of whether they accompany a CV or CVN. And this refueling is accomplished by Combat Logistics Force which usually also refuel the CVs in addition to replenishment of other provision which are also needed by CVNs.
So, at-sea replenishment offsets the CVs limited storage and endurance compared to CVNs.
3. Refueling a nuclear carrier takes about $2 billion. However, in a 40 year lifespan of a CVN, it needs refueling only once. So, $2 billion for 1.5 million miles comes to about $1200 per mile. Compare that with 2.4 million gallons for 4000 miles - at even $3 a gallon (which is ridiculous), it will be $1800 per mile (1.5 times more expensive). Not to mention you have to find a refueling facility every 4000 miles.
So, overall, CVNs are cheaper in terms of operational costs and better for wartime activity.
Here is the calculation of fuel costs of CV and CVN by US GAO. CVNs are expensive again - 738+469 million dollars for CV versus 2045 million dollars for CVN.
You can find more comparisons of CV vs CVN here
http://www.gao.gov/archive/1998/ns98001.pdf