There is a reason why most Dukes for sale are cheap... My next door hangar mate has a Duke and said it's cheaper to fly his C501 than it is the Duke most of the time.
If you must, get one with winglets (so I have heard.)
Probably a little hyperbole in there.
The Duke burns about 40gph (well, 60 first hour, 40 after that). I flight plan at 200 KTAS. On a 3hr flight, I'll burn 140 gallons and go say 600 miles. So that 4.28nm/gal.
The 501 burns 150gph at lets call it 330 KTAS. Let's ignore first hour fuel burn in the Citation, which will be higher. So on a 3hr flight, the citation burns 450gal and goes 990 miles. That's 2.2nm/gal.
Of course, depending on where you're buying fuel, it could get closer.
I figure $5.50 is about average for what I'm paying for AvGas (under $5 near home, but more away from home). I think a "good" price on jet-a right now, assuming you're on CAA, is around $4/gal (for rounding purposes).
Let's also assume I need to cover the 990 miles that the Citation does.
In the Duke, that's a 4.5hr flight (but 2 first hours because the Duke won't do 4.5hrs w/ a 1hr reserve). So the duke will burn 220 gallons to cover the same distance as the Citation at 450 gallons (140 for the first 3 hours, 80 for the second post-fuel-stop 1.5 hr leg).
So for the hypothetical 990 mile trip, the Duke takes 4.5hrs and uses 220gal at $5.50/gal, for a total of $1210 in fuel.
The Citation does it in 3 hours for $1800 in gas.
But insurance, scheduled maintenance, engine programs (for the jet), hangar, etc. for the Citation will be far, far more than the Duke.