Unless your off-roading is in sand, taller tires with the same width are what you want, not taller/wider. Tall, skinny tires will cut through the snow/mud to the "terra firma" below; fat tires want to float on top and don't provide traction.
The (2008 and others) Super Duty will take 34 X 10.50 R17's (BFG All Terrains are my preference) on the stock rims with no lift. 35's would fit, but they are usually (always?) 35 X 12.50's and these wider tires will rub. I've also had 37 X 12.50's on an F350 with NO lift with a slightly outward offset and aftermarket fenders. Remember: lifting raises the CG and makes it more prone to rollovers; cut (or replace) the fenders for clearance when possible. Gain ground clearance with bigger tires, not a lift.

 

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In my previous - which was my first ever - thread, I mentioned how 34X10.5 17's will fit the ('08) Super Duty without rubbing. This is true. HOWEVER: these tires are NOT E load-rated, which they need to be if used on a Super-Duty. You may not even get a reputable tire shop to mount them.

IF you never load your truck to its intended limits, the 34X 10.50R 17's are great. (I prefer BFG All-Terrain T/A's)

BUT, if you will use your truck to carry a camper or other heavy items, then the tire to get is the (BFG AT) 285/70 R 17. It fits on stock rims and does not rub