Well, the EMH is more than just a regular holodeck character. There's an AI capable of learning and developing new neural pathways at the core of his program (which took many years to design, according to Dr. Zimmerman), so theoretically it's possible he could eventually cross the boundary between a program doing what it does and being truly "alive", but that divide is pretty mysterious and ill defined, in general. Based on Juliana Tainer's descriptions of Data's early days, he didn't sound that different from a newly activated EMH (not quite as abrasive a personality, though). It took time for his neural net to grow to a sufficient complexity and stabilize.
It didn't help that Voyager kind of played fast and loose with vague technobabble even more than other Treks, though... seriously, a Voyager drinking game based on when they say "of some kind" can be hazardous to one's health.
Edited by TM2-Megatron, 18 April 2019 - 03:11 PM.