Both 5th and 6th gears in your new truck are overdrive gears. The transmission in your new truck doesn't have a "direct" gear with a 1:1 ratio like 3rd gear is your last truck. 4th gear in your new truck has a ratio of 1.15:1 so that multiplies torque more than 3rd in your last truck. However, with the increased power of your new truck, 5th gear might allow you to have the same performance as your last truck in 3rd.
One point though...even with the more powerful engine in your new truck, some of that will be eaten up by the heavier weight of the Superduty vs the f150. Also the 6r140 transmission will have more parasitic power loss than the 4r70w transmission in your f150. Finally, if the f250 has larger diameter tires than the f150 that too will effectively reduce your final drive ratio.