I believe C & J cut their shoes somewhat fuller than EG. Green's shoes are quite notorious as narrow. Yes, the waist of EG is narrower and more in keeping with the "fiddle back" of bespoke shoes. But that's more a question of aesthetic than actual fit. (I believe jcusey got recently a pair of EG in E fitting and owns also C & J "hand grades" in E. He might be the best person to advise you about his experience with the fit differences between the two makes.)
I have two pairs of C&J Handgrade shoes, both on the 330 last, and two pairs of EG shoes, both on the 202 last. The first pair of C&J shoes was purchased from Ben Silver, and it, infuriatingly, has the American size marked (10D). I'm pretty sure that the actual British size is a 9.5, but I have no idea if the British width is a D or an E. In any event, those shoes are a bit narrow. I ordered the second pair of C&J shoes from Britain, and they're British 9.5Fs. They're probably too wide for me, but the roominess is very comfortable. The first pair of EG shoes is a British 9.5D, and they're even tighter than the first pair of C&J shoes. The second pair is a British 9.5E, and those shoes are appropriately sized for me. Â I'm not sure what all of this verbiage means, but I think that bengal-stripe's rule of thumb that EG shoes are the narrowest English shoes on the market is accurate.