Ok, first I moved your thread to this forum because it's more likely to see input from guys running the varius setups you mention.
As far as ride quality and handling go, you have three factors:
1. Spring design/spring rate
2. Shock design and valving
3. Anti-roll bar mounting/connection
The spring rate is determined by the number, thickness, length, and arch of the spring. Generally for a softer ride and the same load capacity the lift kits come with springs that have more leafs made from a thinner material. This makes the spring more progressive and gives a softer initial compression but ramps up to match or even exceed the factory rate. Also, it's quite common for the spring builders to slip in liners on some of the leafs to increase the slip and remove friction to soften the ride.
Dampers are there to control the axle motion, they need to match the characteristics of the leaf spring and the load or vehicle weight. There are literally dozens of ways to configure the dampers, and I won't get into that. But the best dampers can't cure a ride problem from a spring that's built wrong for the application.
Anti-roll bars or sway bars are really a fine tuning device for the suspension. They work to limit body roll but they can also impose additional spring rate in the process. Changing the length of the sway bar end link does slightly change the rate of the bar, so in actuality it is better to keep the end link the same and relocate the bar. On the 99-04 trucks this isn't practical like it is on the '05+ models. Suffice to say that if you bind any part of the bar, it will mess with the ride quality.
I would look at the leafs on both trucks. The V10 and the 6.0L are actually pretty close in weight, the 7.3 was a bit heavier. The truck that rides better will likely have a spring with more arch, more leafs, and a more progressive pack. It's not always the case, but fits what you described. You may have gotten springs for a 7.3 for that V10 and not known it all this time. Could be a combination of things, but in the end if the BDS setup is what you prefer, you may simply want to change it out.
The Current Truck (Oct-2013 to Present):
1999 (Early) F-350 Lariat, CCLB, SRW, Black/Tan
7.3L Powerstroke, 4R100, 4x4, 3.73, 37x13.50-18s, '05 Axle Swap, 6" Fabtech lift, GTP38 "D66" turbo upgrade, SCT 4-position chip with custom tuning by me, Straight Piped 4" down pipe through 5" dual stacks, N-Fab full length triple steps, Pro-Tech cab guard and tool box, louvered 5th wheel gate, Hella 500 Fog and Driving lamps, much more to come...
The one I'll miss, (Mar-2009 to Jan-2014):
2000 Excursion XLT 4x4
6.8L V-10, 4R100, 4.30, 285/75-18, 271whp / 388wtq
The one I won't, (Jul-2005 to Sep-2012):
2005 F-350 XLT, CCLB, SRW, 4x4 FX4
6.0L PSD, ZF-6S650, 3.73, 35x12.5-18, 4.5" Lift