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I assume you are talking about the V-10 you have been looking at and questioning on.
The standard gears for the 6.8 were the 3.73s with the option to get the deeper 4.30 gears. The deeper 4.30 gears make towing easier and more fun and will also improve your all around performance as the steeper ratio will enable the power/torque from the motor to be better applied (better TQ multiplication) to the ground. Quicker acceleration and better hill climbing especially with a heavy load onboard or in tow.
The reason for the better performance from the 4.30s is that the 6.8 makes it's best power a little higher in the RPM range than where it will be operating at highway speed. The few hundred extra RPMs do make a noticeable difference in the amount of available power on tap!
As far as towing goes, I can give my experience with both gear ratios. Our EX had the 3.73LS originally and with tem and stock 31.6" tires we towed a 9,500lb toyhauler and saw 6 to 7.5 MPG on trips to/from Philly and Savannah GA along the mostly flat I-95 corridor. When we made the gear swap to 4.88s along with 32" tires (for an effective ratio of about 4.80) we saw 9.0 MPG over that same route at the same speeds and trailer weight. The trans stayed in OD the entire highway portion of the trip vs having it downshift with the 3.73 on the smallest hill or overpass. My next two mods of headers and custom tunes didn't really affect the MPGs much, if at all, but they did improve the drivability a good deal. Once we upgraded to the current 35" tires the effective ratio was brought down to the nearly factory option of 4.39. Around the same time we upgraded to a new TT that scales at 11,000lbs and our setup nets 8 to 9.5 MPG on our mostly highway trips. Along with the better MPGs it does a much better job at pulling in the hills (the tunes make a big difference here too as do the headers to a smaller degree).
My stock unloaded daily driving used to get 14-ish MPG with a best tank at 15.5 MPG on a mixed highway/town trip in ME with 6 adults onboard. Now with the deeper gears, bigger tires and 4" lift it gets 12.5 MPG on the highway unloaded with the cruise set at 65 MPH. Some of that MPG reduction is due to those bigger tires and lift, it's not all from the gears. I don't daily drive it these days, so no data on that.
What is the functional difference between gear sets?
We aren't in your head and we can't read minds. We need a lot more info other than what you...well....you didn't give ANY info! I could move this to any forum here at FTE and every single person would ask you what you're talking about and to post more info.
Back when I was looking into the gear change I had a shop quote me $2000-ish for the 3.73 to 4.88 swap, that was for both axles and new bearings and setup. I have seen others around the country mention prices from $1600 to $3000 for similar work depending on location and individual shops. I would strongly recommend using a shop that does a lot of this type work, you don't want this job done almost right.
Another option would be to find a set of used axles with the 4.30 gears, since that was a factory optioned ratio for both EX and pickups they are out there. Then it's simply a matter of swapping the entire housings out which doesn't require the same level of expertise as properly setting up a ring and pinion. That is the route that I took with my 4.88s, swapped the entire axle housing out.
What is the functional difference between gear sets?
Functional difference is a 3.73 gear set will turn the wheels one revelution for every 3.73 turns of the drive shaft and the 4.30 will turn the wheel one revalution for every 4.3 turns of the of the drive shaft.