The KEY difference is that the automatically engaging safety in the Ruger is good enough to allow safe carry with all six rounds loaded.
The Uberti safety isn't. It's a slight step up from the "zero safety at all" of the 1873 Colt from which both guns are basically derived, but it's just not enough.
Uberti is now owned by Beretta. Beretta also sells a single action revolver made by Uberti but to Beretta's specs, WITH the same sort of transfer bar ignition as Ruger has. The Beretta-labeled SA (called the "Stampede") is the second of the three transfer-bar-equipped Colt SAA near-clones, the third being the Taurus Gaucho which is getting a lot of problem reports here and elsewhere. Strongly recommend you avoid the Gaucho.
The Ruger New Vaq is a recent Ruger design. It's smaller than the original Vaqueros, isn't as "tough" (can't take 44Mag-class pressures) but it's also better made than previous Ruger SAs. The New Vaqs are built to tighter tolerances, we're seeing zero differences between cylinder chambers on a given cylinder now that the manufacturing process has changed, and *finally* the chambers line up under the loading gate each time the cylinder "clicks" while being spun. Previous Ruger SAs clicked when the chamber was halfway, which was way annoying.
Now. Your Uberti with the NRA markings is somewhat desirable. You may be able to trade it on a slightly used New Vaquero straight up, or with a minimal amount of money involved on a brand new specimen. Try posting in the classifieds here, or at the sassnet.com forums. Cowboy action shooters tend to like late-model Ubertis as the quality is good (very close to Ruger levels) and the "cowboy games" only allow five-up loading so as not to give the non-safety guns a disadvantage over the safety types.
If you're not into the cowboy games, the Ruger can be modified to hell and gone very easily
. Parts from the rest of the Ruger SA product line drop in - including hammers, triggers, grip frames and action parts. My 357 New Vaq sports a lower-slung SuperBlackHawk hammer and I may convert it to a Bird's Head grip frame.
What else...short form, a transfer bar just means that unless the trigger is pulled all the way back, the gun flat cannot go off. The hammer is unable to hit the firing pin unless a piece of metal is jammed between them "transferring" the hammer's energy to the firing pin. This "transfer bar" is activated by the trigger. If the hammer is struck or slips off the sear without a deliberate firing trigger stroke, it can't go "bang".
The Ubertis have a very small hammer block mechanism but it's a bad joke and NOT something you'd trust your life to. Hence "five beans in the wheel" and carry with the hammer on the empty chamber.