Weber 34 installed for over 2 yrs not and flawless.
I get 24 mpg hwy and the other day it came in at 25 mpg on a trip to get some parts. It pulls and roars from 600 to 4400 rpms. Many post on this forum or made contact in Twin Cities their 258 maxies out at 2800 rpms. I have a Weber 34, Summit CDI, TeamRush, Aux Grounds, Borla Header & Exhaust. I have been around jeeps since the early seventies and I have not seen a 258 run any better than this. For a stock engine internals.... this runs pretty darn well.
I can tune a idle from 450 to 900 rpms so I have adjustment on my idle screw.
A smaller range carb will always run smoother thru general operation situations. The only limitations would be WOT, wide open throttle, and most of us never run these 30 year old CJs WOT.
The Carter BBD can be corrected and modified to work just fine provided the linkage thru holes are not worn oval and just worn out. The Motorcraft 2100 and Weber 32/36 and 34/34 are all good alternatives. There are Holleys too. Lots of good choices!
Good CARB choices will give you 20 mpg+ hwy, decent power, and smooth operation where you want to run your CJ.
I think you will be happy with your 38 choice...... but keep in mind if you want any carb to be tweeked / matched to your engine... you will most likely be changing jets.