Either the F23 or F40 "will work", but the F40 will be 3x to 5x more expensive.
However,
If you want to play around with final drives to better match a high power vehicle, or have more room within the bellhousing to run a twin disk clutch for better holding power and drivability, then the F40 has options that are simply not available for the F23.
Here are the available gear ratios and final drivers for the F40 - however, the final drives numerically lower than 3.545 are only available oversees (but transmissions can be imported).
The F40 also as room for a 9 1/4" twin disk clutch (with a custom flywheel and some slight modifications to the pressure plate) that drives like stock.
My LS4/F40/Turbo is running the 3.091 final drive and a McLeod twin disk clutch.
At 4 -5 lbs of boost, the ecm is showing between 450 and 490 FWTQ from 2700 rpm to 6600 rpm (haven't dyno'd it yet or pushed the boost).
I am easily over $5,500 in parts (excluding labor) from the flywheel, clutch, transmission, final drive upgrade, and axles - but I love how it drives!