I clicked on this thread on the sidebar thinking it was gonna be for a 6" TTB lift lol
Having a good amount of hands-on experience with BDS & Rough Country kits for the Toyota Tacoma, I still should be able to offer a good bit of useful info though.
BDS definitely is the kit with better build quality, although RC is not what I would call "junk" either (not like their TTB kits are), and is less $$$.
BDS has the Fox shock option, which is very hard (if not impossible) to beat. RC has their Vertex shocks, which also are quite good, but not quite on the same level as Fox (they probably don't have as good parts availability for rebuilding/revalving them either).
Both kits crossmembers are made from ¼" thick welded plate, however the BDS's have better, more-complete welds (you can actually see the incomplete on-off-on-off welds on the crossmembers in the stock photo of the RC kit posted earlier), and the BDS knuckles are much beefier. I will say though, the knuckles in the pics of the BDS & RC kits for the Ranger look a little closer to being comparable than the same knuckles for a Tacoma are.
Both kits do lack options for rear leaf springs, but another way to ditch the ridiculously-tall (~4") blocks for something more reasonable, is to find a good set of 2-3" lift leafs and pair them with 1-2" blocks (having custom springs made is $$$$$). Up to 2" blocks aren't an issue (after all, Ford used them for almost three decades on the older Rangers).
As for cutting the mount off the diff housing... With as low-down as Ford put the damn thing, BDS probably thought the increase in clearance was worth doing it that way (in the RC install guide it looks to be hanging at least a good inch below the crossmember). I've seen some guys fret over cutting out the crossmember, but with the new replacement being so much beefier, I fail to see much concern there. Just save the old crossmember if you think you ever might de-install the lift, it can always be welded back where it was (the aluminum diff mount would be harder to reweld and have it be solid though, so probably would want to get a new (junkyard) housing in such case).
After looking at the installation of both kits I now agree that the RC kit is a better option. Less cutting, especially not cutting on the differential. The BDS appears to allow for about 1 inch more ground clearance on the front diff with their installation process is the real difference in my opinion. The other issue I have is the shop says they do not want to put my Eibach coilovers on the lift because they don’t stack lifts, which I understand, but they are okay with adjusting the stock coilovers per the instructions or installing other coilovers ie the Fox 2.5’s from the BDS kit (which I like by the way).
If you want to use your Eibach coilovers with the kit, you'll need to measure the drop-down amount at the kit's crossmembers, then check whether the kit's shock spacers match that amount to within ¼" or so (some (but not all) kits' spacers are significantly taller than the drop crossmembers and so is why your shop would have a concern about it). If the spacers match with the drop-downs, then there should be no problem running whatever shocks you want with the kit.
If they don't match, it might be possible to create suitable spacers yourself using various spacers you can get for $30-50 on Amazon or Ebay and bolting them together.
I don't know offhand what the '19-'23 ranger suspension's motion ratio is though (nor do I have info on the drop crossmembers for either k), so I couldn't tell you which actual spacers to buy (what their actual thicknesses are vs their claimed lift amount), but this should be easy enough to do once that info is known.
FWIW, these kits do not need upper control arms (UCAs), though it still is fine to use them if you want.
The drop-down crossmembers w/taller knuckles are what keep the suspension's geometry with the lift like how it was stock (this isn't the case with lifts that simply use longer coilover shocks that push the suspension (control arms) down for lift... You lose caster angle when you lift it that way, and so is why you need UCAs with a coilover shock lift).
(would anyone know offhand what the motion ratio for the '19-'23 ranger suspension is?)