well, go figure! The one on the right I didn't know of! The one on the left is the official one; it's from it that the stylised red sword adorning the flukes forward of the funnel is inspired. That would be the one used. The one on the left, too would've had two golden 'R's on either side of the St George's Cross, and an 'N' on the bottom centre. I have failed to find out the exact meaning of those letters, since the City of London's motto was:
"Domine Dirige Nos; Lord Lead Us!" - adopted by the Rump Parliament, in 1653, confirmed by King Charles II, in 1661 and hence the city's motto. At least those are the versions I've seen. Another, third version, and that's the one I dabbled with, featured, instead, golden Tudor roses in place of the letters! These would make sense, since the first, historic Tudor, Sir Owen Tudor, was a stable Master at Hampton Court; a position which enabled this Welshman's rise to power and influence, and pawing the way for his son Henry (VII) Tudor to seize power, in 1485, after Bosworth. Really, though, I realise, it appears to be some confusion on this matter.
I'll post one of my early Londons with the CoA that I tried to make for comparison:
As you may notice, this is entirely based on the actual City of London CoA, which your left one is too, but the difference here is, besides the Tudor Roses, that the upward-pointing sword is solid red and stylised, and the cross proper is thicker.
BUt, as usual, confusion or not, your work is as always most outstanding!