Welcome
I run 33x9.50-15 BFG AT/KO on 7" wheel with 6" rear spacing. I have added 1.25" spacers to the front and 3" spacers to the rear, as well as poly bushings for the swaybar and good shocks.
Lateral stability feels good. I do not push limits, so I can not attest to what they may be.
It is comfortable for me. Expedition loaded I am at 5900 lbs. Aired down, a cargo box on the top and swaybar disconnected it handles pretty good. I don't think it would be competitive in a slalom race.
Tires aired up, swaybar connected and "empty" It handles pretty good.
In my case I would say it handles as good as stock despite the size of the tires. The addition of poly bushings, good shocks, rear springs and wider track equaled the perceived loss the taller sidewalls may have given.
In my case performance was enhanced. The "pizza cutters" were lighter than the 31x10.5-15 tires I had been using. The reduced mass make them "snappy". It takes less horsepower to get them going. The height matched the lower gear ratio I have better. The reduced rolling resistance may have been a contributing factor to slightly improved fuel mileage too.
The narrower, lighter tire may reduce the stress on the front steering components, as well as suspension components. I know offroad they float over the terrain very nicely.
With the tread width matching the rim width I can run higher air pressures on the street and not wear out the center of the tread. That helps reduce rolling resistance and hopefully improve mileage.
I would match the tread to the wheel and go with the 33x10.5-15, unless you do slalom race, and then perhaps some taller wheels would be a good choice?