Cones and domes have fundamentally different off-axis radiation pattern. Shortly, domes have smoother off-axis behaviour. On the other hand cones have more effective on-axis radiation area (with same diameter) which helps in low end of passband, higher spl/less distortion. Difference in "sound" is not so big, if any, unless either one is pushed out of it's comfort zone.
Legendary
Zaphaudio measurements, first 3" dome , then 3" shallow cone
More basics from Klippel
https://www.klippel.de/fileadmin/_migrated/content_uploads/KLIPPEL_Sound_Radiation_Poster_01.pdf
We have some modern large domes, eg. from Devialet and Accuton.