I don't remember the details of Moriarty's holosim. Was the bread-box-sized device intended to be a backup of him that had to be hooked up to other hardware to function, or was it completely operational on its own?
If recall right the portable emitters were also self contained. The villain actually yanked the EMH out of Voyager and into the portable emitter. Even the non-future tech ones were only about the size of a basketball.
Id have to look up the episode to be sure. But if I recall right it was Moriarty and co's actual programs, not backups, somehow now in that box sized simulator. And it was self contained. Think they put it on a shelf? All indicators was they were in there puttering around a fully simulated universe all housed in that box.
But none of its ever been consistent and depending on the writer its all over the place whats doing what when where and how. Voyager especially played fast and loose that that. DS9 toyed with it on rare occasion but had bigger fish to phaser.