Hi Noonenosthis1 (Shrtmen), Plenty of opinions and advice from owners who have made the gear change. So I'll add my opinion here just like I did over on the Excursion forum.
Your 3.73 gears will get you to where ever you want to camp, but you will climb the hills more slowly and use more gas getting there. You will also be putting more stress on your EX's transmission with the 3.73 vs deeper 4.30 gears. I'm not saying that it will outright kill the trans in a single camping season but that trans isn't getting any younger and it has a few miles on it by now. The 4R100 transmission, like most others hates heat more than anything else, every time it needs to drop out of OD while towing to climb a hill it will build additional heat, additional to the heat from towing the heavy TT. There are two great ways to beat that heat, swap in a larger trans fluid cooler, the cooler from a 6.0 diesel EX or Super Duty is a nearly direct swap and will provide about twice the cooling capacity over the stock V-10 cooler. The other way is to keep it in OD and the torque convertor locked up more, the deeper gears will do this. The toque convertor will unlock whenever the trans shifts up/down, even these brief unlocked periods will add heat to the fluid due to slippage. The amount of additional heat is influenced by the ambient temp, load, RPMs and fluid condition. The trans will generate less heat when in OD than it does in any lower gear.
The V-10 is by design a high revving engine that makes it best power at what would be higher than "typical" highway speeds when in OD with 3.73 gears. Ford chose the 3.73s to be the standard gear for these giant wagons for better fuel mileages when used as daily drivers. They also offered the optional 4.30 gear sets for those owners who planned to tow with the big wagons and wanted to get the engine turning up in the slightly higher revs that would make more power available for the towing work. As was already said, a few hundred RPMs can make a significant improvement! These deeper gears will also allow the combined weight of EX and trailer to get rolling from a start more easily due to the increased gear multiplication.
So I too will join the group recommending the 4.30 gears if you are staying with the stock 31.6" tall tires (265/75R16). To get a better performing tow rig that will climb hills more easily, accelerate better, put less stress on the trans and build less heat there all while getting better towing fuel mileage 4.30s are the answer. You may see a 1 to 1.5 MPG drop in unloaded highway mileage with the new gears but many have reported the same to slightly better in-town mileage with them.
When I first made the gear change I made an even larger jump, I went from the factory 3.73 to 4.88s. At that time we were towing a 31' 9,500lb toyhauler up/down the East coast frequently. Pre-swap we were getting 6 to 7 MPG on the trips, on the first trip with the new gears over the same route at the same weight and speeds we got a solid 9 MPG with no other changes besides the gears. The towing performance was greatly improved and where the 3.73s had the EX/TH combo downshifting if we ran over a shadow (a main contributor to the low MPGs) it didn't downshift a single time on the highway from Philly to Savannah and back. The unloaded MPG dropped from my typical 50/50 mix of 14 MPG to 12 MPG with the 4.88s. Since that time I have upgraded the EX with a 4" lift, 35" tires, Headers and custom tunes. The taller tires drop the effective gear ratio to 4.39 and it now gets 12.5 MPG, but the big tires and lift is eating into the MPGs some. Towing our current 41' 11,000lb TT we are seeing between 8 and 9.4 MPG on our mostly highway towing trips. The 4.39 ratio handles the big TT's weight with ease, only dropping out of OD on the bigger Interstate Highway grades while maintaining speed. It's a great combo for our heavy towing work.
I am still running with the factory V-10 trans cooler and have only ever seen the trans temp climb over 200* twice while climbing very steep mountain roads in VT on a hot day. I have the new 6.0 cooler in my garage waiting for the time to swap it in to be better prepared for future Western mountain trips. I would recommend getting some way to monitor the trans temp while towing, I use a stand alone gauge but there are plenty of OBDII options with Apps on smartphones and tablets. Catching a hot trans early can save you a major and expensive repair bill.
Custom tunes are another great upgrade for a hard working V-10, 5Star Tuning knows these rigs very well and offers excellent service. Super easy to install and use the tunes too.
Good luck and happy camping!