I was able to pick out my own new company truck back in June '06, as long as it was off the Ford lot. I picked an '06 F-150 Super Crew Cab (full 4dr) , bright red with factory 20" wheels and a 6'3" bed.
I just now changed employment to a different company (doing the same job) and my new boss/ owner gave me his personal Dodge Ram 1500-'06 bright red 4dr with factory 20" wheels. Ha! Same exact set up but a Dodge. Oh, and its a Hemi.
The first thing i noticed was how incredibly fast the Dodge is. Wow. Great throttle response off the line from a light: just barely touch the pedal and it zooms away effortlessly. The torgue is always there at any rpm level. Its amazing how it gets out of those 65 mph traffic clusters. (My wife raced me in her '04 Nissan Murano - a little performance machine in its own right- She jumped me on the freeway from 70, getting the Murano's midpoint to the Dodge's front bumper, but the Ram quickly caught up and pulled its midsection to the Murano's front bumper by the time we hit 100- for research purposes only of course.:ylsmoke
The 300hp Ford makes a good sound when you punch it but just didn't respond. With a quick glance at F-150 forums, I'm sure there is a ton of aftermarket performance available if thats your thing. We have a 4500lb camper trailer and the 5.7 F-150 hauled it over the mountain pass comfortably with no problems. (A racing acquaintance happenned to be behind me on the mountain pass in his Powerstroke Sportsmobile and later commented on how my rig was moving along at a nice clip.)
The second thing I noticed is how bumpy the ride is. The F-150 ride is smooth and soft, great for going over the mountain pass. I haven't driven the Dodge with anything more than my GasGas 450 (250lb enduro) in the back, but its a stiff bouncy ride.
The Ford seating position was slightly more comfortable for me (5'11, long torso, short inseam).
The F-150 had a ton of room in the back seat for adults; my friends where pleased on road trips. The Dodge not as much.
The Dodge reminds me of my '98 Dakota in the fact that you always feel like you're driving a muscle truck; fast and responsive, and I'm going to get a ticket if I'm not careful. When the Ford was shiney new, a realtor acquaintance approached me at a jobsite and commented he had just read in Forbes magazine that more millionaires drive Ford F-Series than any other vehicle by far (random factoid for whatever it's worth).
I turned the Ford in with 50k miles. Problems in that time were a power window, catalytic converter, surging brakes (felt like warped rotors), all warranteed.
The Dodge has 40k on it now and I'm not familiar with its history as I just took it over at Thanksgiving. It seems fine.
Traction: We live on a very steep hill and Bellingham does not know how to clear their streets like the midwest towns I've lived in. (Of course I rather enjoy that little fact about Bellingham:wings

The Ford came with Pirelli Scorpian ATRs. I was amazed at how well they did on ice and snow, and at muddy jobsites. The Dodge has Goodyear Wranglers and all I know is, at 40kmiles, the don't look too bad, but it spins at the bottom of my street when its wet out. Maybe its the combination of 40k miles, and the torguey Hemi, but I actually don't fell safe pulling out in traffic on wet days. (I've shifted into 4 hi twice at stop signs to be able to pll out safely, then back into 2 hi on the fly)
The Murano has 18" Toyo Proxy ST's with 30k on them. It will get Pirelli's when the time comes.
Oh, and if you are going to hual a small fifth wheel camper, make sure that you check to see that the bed walls on the Ford are not actually too high.
Overall, I don't have a clear preference. Maybe because I don't have to make a choice and pay the bill; it's been decided for me. Both trucks are more than fine. I suppose if i did have to make a choice, it would come down to finding a better deal on one of them, to save money for spending on my van, my bikes, and our trips.
Edit:
Ford F-150 Electric Transfer case experience: I pulled into a jobsite once and an inspector pulled in rihgt behind me so I drove down a slope of compacted ABC (dirt/ gravel mix for driveway sublayer prep material ) a little further than I thought I should, but it is a 4x4 so i didn't worry too much. I was the last to leave and no matter how easy I was on the throttle, I could not reverse up the incline without digging down into the ABC mix. While stuck, I could not get the electric t case to engage. I was there for about 20 minutes going back and forth just a little further each time gently making my own trench out. I finally got out without ever getting the front axle to engage, trying both in neutral and in park, (even driving forward to satisfy the 15' needed to engage rumour). Later, the dealer said it was fine and I just didn't know how to engage it-even though after the first ten minutes I actually got out the manual to see how the heck I was turning the plastic dial wrong.

Nothing like having almost $40k of 4x4 capital sitting there and not being able to use it because of an electronic malfunction of something or other that doesn't seem to be broken until you actually need it.