Your theory has merit, considering the Binars were able to both run the holodeck and backup their entire species to Big D's computer.

However, the EMH was developed on Jupiter Station which is significantly larger than the Enterprise D and as such should have a ton of computing power. But maybe that was being used for other stuff, which is why he was so frustrated all the time.

It is 8 years older though. I dunno if Federation computer still follow Moore's law, but that makes Voyager more capable.

Yeah but does it have bio-neural gel packs? Noooope