-The crew would be more three-dimensional. Character development would be consistent.
-Neelix would be cool. He might even wear a bowtie. I wouldn't even bother with Kes.
-Anwar, I really like your idea of the other crew being Romulans. Most of the conflict with the Maquis felt forced - as mentioned before, they are Federation citizens. But for a Romulan crew to join forces with the Federation would be a lot more interesting.
-Romulans or otherwise, I wouldn't combine the two crews right away. The Romulans would have a small scout-ship sort of vessel and Janeway would offer to work together, but being Romulans most of them would refuse and do their own thing. In their respective searches for information, the two crews would eventually meet up. I'd have Voyager find the Romulans in the middle of a firefight and decide to intervene - the Romulan ship would be destroyed, Voyager would take on heavy damage, and the crews would be forced to work together.
-The crew would have no idea where they were. A major part of at least the first season would be gathering information and getting to know the area of space they were in.
-Voyager wouldn't stray into Borg territory - instead, the Borg presence in that area of space would be Voyager's fault. They'd find a drifting Borg ship and try to scavenge some technology, inadvertently activating it's systems once again and bringing its drones out of stasis. It would look around and tell the rest of the Collective, "Hey, look what I found! Some lovely advanced civilizations! Let's eat."
-The 8472 would be known to the residents of that area. (They'd probably call them something like The Really Scary Monsters Over There.) They'd make occasional forays into normal space from their fluidic realm, but nobody would know why. Then the Borg would try to assimilate them...bad idea.
-The entire area would be torn apart by the Borg-8472 war, and Voyager's crew would try to make up for their mistake by organizing a temporary (at first) Federation to stop both the Borg and the 8472. They'd retrace some of their earlier steps and call upon the races they encountered (both friendly and hostile) to help them turn the tides of the war.