"Which full-size SUVs come close to the 2014 MDX's mileage?"
If by "full-size" you mean body-on-frame SUVs such as the Chevrolet Tahoe and Ford Expedition, none comes close to the redesigned 2014 MDX, which has impressive fuel-economy ratings for a three-row crossover.
The new MDX carries less weight and uses a more efficient engine. EPA estimates for the all-wheel-drive MDX are 18/27 mpg city/highway, and the front-wheel-drive MDX is even better at 20/28 mpg.
Those numbers — which are estimates, not promises — still look impressive compared with other large, three-row crossover SUVs. All-wheel-drive models that beat the MDX's numbers include the Toyota Highlander Hybrid (28/28 mpg) and the Audi Q7 TDI diesel (19/28 mpg). The BMW X5 xDrive35d and Mercedes-Benz GL350 Bluetec diesels come close at 19/26 mpg.
Several gas-only three-row SUVs have EPA highway ratings of 26 mpg or higher, including the Ford Explorer, Kia Sorento and Nissan Pathfinder, but only with front-wheel drive or a four-cylinder engine. The MDX comes with a standard 3.5-liter V-6, and even the all-wheel-drive model has higher fuel-economy ratings than some front-wheel-drive SUVs with three rows of seats.
The Cars.com Vehicle Recommender, found here, should be able to help you sort through the many SUVs available to find the ones that offer the fuel economy and features you want at a price you can afford.