Are two twin-jet flights more efficient than one quad-jet flight?
The sales figures tell it all. The majority of airlines prefer twin-jets. From businessinsider.com:
Qantas CEO offers his insight on 2x 787 vs 1x A380:

According to [Qantas CEO], he can fly two 236-seat Dreamliners for less than the cost of a single 486-seat A380, which entered the Qantas fleet in 2008.
&quot;If we were to fly two 787s tail-to-tail, the per-seat cost would be less than the A380,&quot; the Qantas CEO said.

Even though the 787 has a newer generation engines compared to the A380, the fact that the 747-8I (the passenger variant) didn't sell well confirms the above.

(wikipedia.org) Fuel per seat figures for a 7,200 NM sector.
A major issue in comparing is finding:

A twin whose ideal seating capacity is half that of a quad
And boosts the same range
And be of the same generation.


(DVB Bank SE)

See: Why are twin engine airliners more fuel efficient than three or four engine airliners?

RE edit and comments:


As one concrete example, say one A-380 @ 15000 km and 650 passengers vs. two A-350 @ 15000 km and 325 passengers each.


They fail one of the conditions above, the 350 and 380 have different engine generations. And it's like the Qantas 787/380 example above.



Would there be a twin &amp; quad combination with roughly the same age?


The A330-300 (twin) and A340-300 (quad) are the same age, and even better they share the same fuselage, wing, and total thrust, but they too fail one of the conditions: the A330-300's range is shorter than the A340-300's.
The A340 has longer range because the outboard engines on the A340 increase the bending relief, allowing 30 tonnes more fuel (flightglobal.com):

Because of bending relief from the weight of its outboard engines, the bending moment of a four-engined aircraft is substantially lower than it is for a twin at the same maximum take-off weight. For the same fuselage weight, therefore, a twin needs a stronger, heavier wing than a quad.
It follows that, for the same wing, the payload carried in the fuselage must be less for a twin than a four, which is exactly what has happened with the A330/A340: the latter carries about 20% more payload. This translates to about 30t of extra fuel, giving the A340 its long-range capability and requiring the addition of a centre-fuselage undercarriage leg. Design strength required was &quot;only 1% higher than the A330&quot;, says Jeff Jupp, BAe chief engineer, Airbus.

The A330-2/300 sold 5.87 times more than the A340-2/300 (now out of production) as of end of March 2018.



What about a 767 vs 747 limited to the 767's range?


Limiting the 747 to the 767's range is again not fair, because of the fuel the 767 will have to carry to reach its max range, while the 747 will breeze by because it won't carry its full fuel load. See this related post: How much fuel is burned to carry the trip fuel?