Your question might be better phrased as "big shock or little shock", since there are more than Camburg and Bilstein offering shocks. Personally, of the smaller bore shocks, I'd recommend Bilstein. Of the larger bore, IVD or Camburg...they really are "all mountain" shocks.
It really comes down to how you choose to drive, offroad...onroad, I doubt you'll notice a difference. If you're a mellow driver and rarely (if ever) push your truck either to extremes of articulation or extremes of speed, and you only use the truck lightly loaded for day trips, the less-expensive Bilsteins will suit you just fine, and there is a 5100 kit designed specifically for your truck.
If you see a need for improved articulation, either the Camburg or IVD extended coilovers along with Camburg's upper control arm will do the trick. Bilstein does not offer a similar option that I am aware of...while they offer a larger bore coilover, I've never heard of a Tundra-specific extended option for use with the high-misalignment joints in the aftermarket upper control arms.
The other benefit to the Camburg and IVD coilovers is the spring rate of the coil itself, which I've found much better suited to a loaded truck and offroad use than the stock coils. In addition, if one spring rate doesn't suit your truck, there's probably another that will, unlike the 5100 kit which uses your stock coils.
I have found in the past that proximity to Southeast Utah results in a lot of baked shocks

, and baked shock oil is one of the worst things I've ever smelled. You're quite capable of baking the stock shocks, non-resi Bilsteins, OMEs, and 2.0" non-resi versions of the larger coilovers, on the exit from the Dollhouse to Hite Marina (that is a great drive, BTW!). I don't doubt we have a few routes here in CO which will do the same, if you get moving.
Your truck, in stock form, is capable of a lot...including runs which require dozens of miles of moderate to difficult 4WD and dozens of miles of 2WD at speed. Plenty of routes in CO are the same way...you can take a Subaru (usually) over Shrine Pass, and I suspect if the trail's in good condition, you could take a Subi with a decent low-range tcase over the McAllister Gulch trail...but you can do it twice as fast in a truck with good suspension. It's worth spending the money for the larger coilovers...you're getting far more than just a desert-appropriate coilover, you're also getting greatly improved load handling, resistance to fading, and with a Camburg upper control arm, extended travel.
As much as I like and recommend IVD, everyone else will
also say that they designed their product from the ground up, specifically for your truck

.
(Sorry Mike

).
Both IVD's and Camburg's products will excel at high and low speed trails. Both offer excellent customer service, a long history of desert racing experience, and top shelf products. Pricewise, they are currently close enough through Wheeler's to be effectively the same.
If you're not familiar with the difference between digressive and linear pistons and why you might want one vs the other,
this isn't a bad place to start. Personally, I would call that the biggest difference between the two products...as far as I know, Camburg's version of the Swayaway still uses a linear piston (I haven't taken mine apart to look, but you can certainly call them, I'm sure they'll tell you).
I like them both, and I get a great impression of both companies...they're very supportive of the Toyota offroad community. Pick a color and get to driving


. Better yet, support both and get a Camburg upper arm with an IVD coilover

.
Dunno if you've met any of the COTTORA crowd yet, but we'll be down in the Springs on the 28th for a benefit wrenching event...drop in to the COTTORA forum if you haven't already

.
-Sean