I've had some rare skinnies and plenty of fats.
These include:
33 x 10.5 R 15 BFG AT Toyota Pickup
33 x 9.5 R 15 BFG AT FJ40 Land Cruiser (heavy), FJ60 Land Cruiser
33 x 12.5 R 15 All Terrains and Mud Terrains FJ 40 Land Cruiser (heavy), FJ60, HJ60 Land Cruiser
Michelin XZL 9.00 R 16 (ala 36.5" x 9.5" R 16) FJ55 Land Cruiser (heavy, SOA)
34 x 9.5 R 15 Super Swamper TSL Radial FJ40 Land Cruiser (very heavy)
35 x 10.5 R 15Super Swamper TSL Radial FJ40 Land Cruiser (very heavy)
35 x 12.5 R 15 Goodyear Wrangler AT FJ55 Land Cruiser (heavy, SOA)
35 x 12.5 R 15 Goodyear Wrangler MTR FJ55 Land Cruiser Heavy, SOA)
32 x 11.5 R 15 BFG AT, Big O AT, Toyota Pickup
285 75 R 16 Snow King Radials
These are all my different tires for about the last 10 years in a wide variety of applications from Muddy Woodsy back east to the desert, mountains, snow, sand, and slickrock out here...
Pardon this long rambling thoughts I'm basically thinking out loud here but this is real experience with the above tires and comparing skinny to fat.
Basically there is no magic formula for everything unfortunately and there are lots of variables including vehicle and rim width in particular, and diameter (bigger is generally more stable). I am definitely a fan of tall skinnies and I believe I've owned an impressive list of some of them. I have had good results but truthfully looking at them I'd say I've had bad experiences more often than not... For example now that I think about it, I've never worn a tall skinny to death unlike a 35 x 12.5 R 15 actually.
I have used several sizes including "wide" mostly out of availability. I really liked my 33 x 10.5 BFG AT's the last round but noticed that if I towed a moderately heavy trailer it would wiggle around and get unsafe as speed. Otherwise they were quite stable. I feel like there is a magic balance that can be found between width and stability. It is narrower than the 12.5s that are popular (where Scott's point really has vailitity) but 9.5 is too narrow for pretty much anything. I feel that 10.5 cuts the mustard just fine if you ask me.
On my pickup with wallowing when towing a heavy trailer (for example our '73 Travel Trailer) or I downgraded to 32 x 11.5 R 15 the problem went away and I also had noticeably more power and some of the best economy as well. In that case the 33 x 10.5s were a liability. There were only a few situations where they were a better tire, which were unloaded and off road only otherwise the 32 x 11.5 were are superior tire pretty much universally.
The 33 x 9.5's were particularly bad and if the vehicle had any major load the truck would sort of wallow around, definitely the wrong tire for the wrong ap. This is with FJ40 and FJ60 applications. Quoting some very knowledgeable friends I remember them saying "you don't want a pig like a FJ60 on a 9.5 tire. It will wallow too much." They were right.. I would recommend a 33 x 10.5 any day of the week over 9.5 and for all applications. It is still pretty tall and skinny. I was using 6.5" rims though, 7" would have been better for 10.5s though, and the narrow rim accents the (negatives of the) narrow tire even more.
Back east tall skinnies are very very nice mostly because there is so much mud. They go right to the bottom of the mud and find traction and this was always great. Back east because there are so many trees you want a low vehicle. For hard wheeling you still want large tires so you want to trim otherwise your roof, windshild or roll bar are constantly rubbing on trees. This is one location where the Super Swamper 34 x 9.5 really really shined.
However I have also had the most bead popping issues with tall skinnies (for example a stick sliding between the tire and rim and blowing a bead --- this doesn't happen with fat tires) and most importantly tall skinnies also lack sidewall stability, no matter how thick they are made. I nearly rolled on my Michelin XZLs (36.5 x 9.5 -- an extreme tall skinny example -- a military tire app) because my rear end slid off an obstacle and the vehicle started moving laterally because of tire sidewall flex. These tires are also built like tanks...
I used my soa FJ55 as a daily driver, towed vehicles, I also nearly doubled its own weight with a load including 400lbs on the roof to Burning Man and back once. Tire of choice there was quite "fat" (So I was on 35 x 12.5 R 15). Mostly because I wanted 35" and this is my only option other than a Swamper. Swampers are great for their application but they suck on the road, even radials. They are not an "expedition" tire at all unfortunately.
This is wider than I would have liked, mostly because of economy. Wider tires make a big wide path for the wind to get shoved around from and take quite a bit of strength to get around. It is actually the full size pickup guys who have the best info about what a 35 can cost you mileage wise, which is usually at least 2 mpg. A 2000 Ford Super Duty for example, 16 mpg to 14 mpg because of fat 35s (stupid, if you ask me). I also very much liked my Goodyear MTRs in 35's but they singlehandedly cost me about 2 mpg (considerable loss -- but only down to about 22 overall MPG on my diesel FJ55 down from 24-25 mpg on average) from the 35" ATs I had on before. So Mud or All Terrain made a big difference.
But the truth is this tire size is very stable laterally. It is also a "wide tire" but it also provides excellent traction particularly in the west. I cannot say why but I've found 35 x 12.5 MTR and Goodyear AT stick like glue over everything among the best I've ever used. With a heavy load out west tall skinnies really wallow a lot over technical wheeling and also wallow with a load.
Also this tire size (35") is "just large enough" to get over anything with western style wheeling. So this is my tire of choice for any vehicle that gets "off roaded" here in the West as I find I can just barely hang with the big boys but load the truck up drive it there and drive it home and use the vehicle as an "expedition vehicle" or at least in the mindset we all have. I would say the same of a 33 x 12.5 as well unfortunately, though they are ballons... 32s and 33's which are popular here are usually overkill for most dirt road and rough dirt road driving, good for some random obstacle or really bad section that might come in your way, but are almost too small for a lot of technical stuff that really embodies much off road terrain around here except for groomed off road trails like Moab, etc...
One thing is correct rim width makes a big difference. 10" rims? Not for me, 8" on 12.5's all the way. The best overall performance, wear, tire profile combination, and bead strength positioning...
However testament to Scott Brady's arguement.. 12.5's in snow? Awful, complete lack of traction versus a tall skinny. This is where his co-efficient really makes sense and you can see practical sense of it all... Tread pattern also makes a big difference there but a wide tire in snow is a compromise, period.
My own conclusions? Good question... There is no magical formula, again it depends on your vehicle..
On my new FJ55 (that will hopefully be completed in the next year, full resto, diesel, locking differentials, modernization, etc) 35s x 12.5's x 17's this time is what I decided. They are metricl BFG AT's that are "305s" so a hair narrow technically but are basically 35 x 12.5 more or less. This is if I want to be able to drive to Moab or other areas and back, get decent mileage with the AT's (25 mpg with my diesel again), but be able to hopefully do a trail like Pritchett Canyon there which is among some of the hardest trails in Moab. My other consideration is 255 85 R 16 which is a tall skinny that is about 34 x 10.5. They make an E rated version as well.
My gearing will allow for more power but a poorer overall top speed (which is important) down to about 75 mpg instead of 80-85 which is good and important and even legal here in Utah in some places. This is largely related to the diesel as it is designed to be geared well with 4.10 diffs and 35" tires.
I hope it helps!