Maybe a helpful thing to remember is that Shoei fits oval/rectangular heads and Arai fits round heads. HJC is kinda in the middle.
I think that is actually mostly backwards. Arai is the only company that differentiates clearly between the product lines/helmet shapes and, therefore, the only one that reliably advertises which one is which.
Signet/Profile/Viper are the long-oval shaped helmets. I know, because that's what my head looks like and it used to be the only helmet that fit me properly.
Vector/Corsair have an intermediate oval shape.
Quantum has a round-oval shape.
I've found most Shoei's to be somewhere between intermediate-oval and round-oval, except that the new RF1100 is more long than intermediate-oval (but the RF1000 is definitely more round - I could never get a good fit in that, even with different thickness cheek pads).
HJC's are mostly round-oval, but the AC series used to be between long and intermediate oval (I have an AC-X3 dirt helmet that fits perfectly, but can not wear most other HJC's I've tried)
I wear a medium Arai and same size Shoei (when they fit
). But, this will vary depending on how well your head fits a particular helmet shape.