Is it worth mentioning that DS9 introduced cannon that prevents a decent EMH/DS9 crossover? The EMH would have been stuck in Quark's.
Doctor Bashir, I Presume
BASHIR: A holographic doctor can literally replace a starship's medical officer during an emergency.
ZIMMERMAN: I'm surprised you don't have one on the station.
SISKO: The station facilities are Cardassian in origin. Most of our equipment is incompatible with Federation technology.
And from The Search
, Bashir doesn't make the Defiant's sickbay sound as advanced as the average SF except for its battle systems. No mention of holo-emiters until they use the silly communication one for all of 2 episodes.
IMO, any attempt of a Voyager/DS9 crossover would come off forced or simply bad if they resorted to all holograms. I guess Q could have done it and pit the two crews against each other in some silly scenario. Might as well add send Picard, Bateson, Kirk, and Garrett invites at that point.