I think it's a matter of flavor. The only person I know who has used EL84 in Aegis is
@goldwerger . Generally though, lower power / current tubes are going to have lower peak power output and a slightly higher output impedance. My very limited experience using 6V6 in Aegis is they don't quite compete with the higher power tubes like EL34 / EL37 in terms of soundstage, clarity, etc. but they have their own enjoyable sound and great tone. The 6V6 I used were the Mazda 6V6GT.
As far as the power output, with peak output being less, probably isn't going to be noticeable with 99% of headphones, only place where it MIGHT matter is with the really demanding stuff, like Susvara and Tungsten. But I think that would need to be confirmed, I don't own either so I can't test myself, it might be just fine.