Hey, Dude, you are moving into Numismatics... LOL. Gimme some History... But the coins are beautiful!
I agree with 4to2 - what is suggesting to you that these are the same hand? Works of art can linked together or to certain artists by focusing on minute diagnostic details - the curl of an ear, the thickness of a serif. Larger aspects of the design could be a result of using the same model, or simply the hallmark of the more general style. The methodology itself was pioneered by Giovanni Morelli in the 19th century and later applied by John Beazley to Greek painted ceramics. It is a bit risky to apply to numismatics. Many of the details on coins would have been officially standardized by the issuing authority, making it difficult or even impossible to determine a particular engraver. IMO, unless you can point out distinct diagnostics and demonstrate their repetition throughout a series of dies (ie, this needs to be done AFTER a complete dies study), then you can't prove much.
The portrait looks very similar, but I've had too much paleography pushed in my head to ignore the writing. Some of the letters look similar, but the very different 'o's makes me think two different people. Also the 'E's - the first coin has a long ligature at the top, whereas the second coin has a long ligature on the bottom. (Although I'll admit that carving dies and writing are two very different skills...)
Thanks for the insight guys. I didnt realize it at first but it did look uncanny in the similarity between the bust of Roma and that of Diana. The relative size, shape of the cheek and jaw line, the height of the relief as well as the relative positions of all the features of the bust. I was think the obverses were done by the same person but like you all stated it might be impossible to know for sure with reasons given. I thought it was enough to at least ask the question.
We have trouble seeing the difference between the same hand and a style similaity caused by both cutters being trained in the same 'school' that certain things are done certain ways. I enjoy looking for similarities like this but am never absolutely sure I know what I'm seeing. Some things could simply be two cutters each trying to please the master by cutting the nose the way he likes it done. I agree there is a possibility but see it as unprovable either way.