I ran 3.73 gears and 33's on my 98 4.0L 4x4 with 5 speed, I didn't like it much.
If the truck is strictly driven on the road and you don't tow or haul much, it won't be that bad. Driving up bigger hills, I had to downshift to 3rd with my manual trans.
Anything offroad that actually requires 4x4 will require 4x4 low (deep snow, mud, sand, etc). Trying to get a trailer moving from a stop is miserable. The auto will do it but it will heat up a lot. If you do it, definitely get a bigger trans cooler.
4.10's would be alright, 4.56 would probably work pretty well. I ran 4.88's on 33's with the sport trac (4.0L sohc automatic) and I loved that setup when I lived in Oregon (lower speed limits). The OHV doesn't like to rev as high as the SOHC, which makes me think the 4.56 would be tolerable and more ideal IF you have the truck offroad and/or tow. Especially if the truck isn't your daily driver. Re-gearing is going to cost a lot, and I wouldn't spend that kind of money JUST to get 4.10 gears. Just my opinion.
2006 F150 FX4 Super Crew - Bilstien 5100s leveled 2", 35" KM2s, 4.56 gears, Detroit locker, Eaton E-Locker, Traction Bars, AEM intake, Xcal 2
2010 VW Golf TDI 6MT