No bad idea to get a Moto G (a lower-mid end device) if you already have an S3 (flagship device, despite not new), unless you have zero intention of ever using the camera on the Moto G at all, it lacks LTE as well.
It's still better to get a used Nexus 4 for the same price as a new Moto G, the N4 is more powerful and is a true Nexus with unlocked bootloader therefore offers more freedom. The Moto G do have one thing the N4 lacks which is USB OTG (plugging in a flashdrive to the phone).
I personally would stick with the S3 because I had it before (but the quadcore international version), but I guess the dualcore ATT version in term of performance it is not too bad compared to the N4. The hardware is fine, its just the Touchwiz bloat that slow it down. The S3 offer more storage than the N4 since it have microSD. With the N4, you are stuck with 12.95GB (the other 3GB is reserved for system). It also have a better camera and removable battery that last slightly longer than the N4. I would look into unlocking the S3 bootloader and install custom roms like CyanogenMod, which offer similar experience to stock Android.
The reason I chose the Nexusis because of the unlocked bootloaders, lots more developers for it and freedom to do what I want and always getting the latest Android version. But you get downsides like less storage, battery life and not the best camera. This aspect has been true for every Nexus phones I owned, they're not phones made to be the best and compete as flagship devices (although the N5 do have the fastest cpu when it was released, it lacks in some other aspects like speaker and camera), but are great values with bootloader and sim unlocked and more freedom.
However, if money isn't an issue, I would just go ahead and get a Nexus, but don't dismiss the Moto X as well, it have some unique features that even the Nexus 5 lacks.
There are lots of Nexus being sold on swappa.com as well.