Is the Metro a better choice than the bus?
Buses are actually supposed to be the accessible choice, with no need to go underground or back up. They are a bit slower and vulnerable to traffic (just like cabs) but if the main concern is minimizing the distance you have to walk with your luggage, then the bus is usually a good choice. In general, taking the metro means risking having to go up and down stairs, but the connection you found is not a metro: it's the RER, and the most modern part of the RER network.
At gare du Nord, there will be escalators but you would arrive relatively far from the mainline platforms. There is, however, a kind of shortcut to avoid going back to the main concourse: an underground passage midway through the platform that you can access from the underground commuter train station, across from the exit of the Magenta E station. It's not an option for all trains; Eurostar trains to the Benelux are not displayed in the underground passage.
No matter which path you choose, if you go with this solution, I would aim to be there a bit earlier than 6 AM to have time to orient yourself and walk back to the mainline platforms.
and wondering if I can pay bus fare with metro tickets by tapping my iPhone?
No, you cannot pay the bus fare with metro tickets, you specifically need bus/tram tickets, which can be loaded on the same virtual transportation card on your iPhone and coexist with metro tickets (but not with airport tickets).
In the absence of information, I suppose that a cab is the smart play.
Taxi is almost always more convenient and easier to figure out, traffic is not a concern for this route at this time of day, but public transportation is perfectly doable, so there is no reason to consider a taxi if you would not otherwise use one out of convenience.
