SIII does have 2G. In today's climate, that is not an insignificant difference... apps have grown and people are getting used to multitasking with them more and more. Between that and the fact that the G hadn't come with LTE capability puts it just a slight tick lower than the SIII. And the X and OnePlus (and M7/8, and Nexus 5, and G2, etc) all those flagships released SINCE the SIII do all have superior stuff under the hood, but the OP wasn't asking about the top of the line models. They were just seeing if they wanted to save some money, would it be a mistake to go with an older model.
Now, i am not blasting the Moto G. Not in even the slightest. I think what Motorola is doing with the lower-end market might possibly be MORE important than the spec wars up top. It wasn't that long ago that even the crappiest smartphones ran into the $300/$400 range. I had a Samsung Galazy Stellar, which had a full retail price of something like $429 (if memory serves me right) and released around the same time as the SIII. No one, of course, paid that price and VZW gave them away with a contract... It was a decent phone, LTE, etc... but that phone was, in every way, shape and form, inferior to it's SIII big brother. Flash forward and my Nexus 5 absolutely destroys that Stellar (and the SIII for that matter) and cost $50 some-odd less.
I think it shows just how far we've come that a $200 device, considered a 'value' model, compares well to phone that was THE phone to have two years ago and came with a $650 price tag. That's nuts. And the Moto E... at $129... it is a phone that seems kind of like a current day version of my Stellar, but $300 less.
OK, bit of a tangent there.... but long story short, I don't think anyone looking to save money would regret getting an SIII.... But if you were looking at anything older than that, go with one of those Motos.