O'Brien: I believe Counselor Troi is the senior officer on the Deck. She carries the rank of Lt. Commander.
While one may argue that Starfleet organization is different from modern military organization, in actual fact this part of it is unlikely. Many officers are given a certain rank which allows them to command others, but for any ship there is a structure called "line officers", which are people specifically trained in ship's command and operation. Troi, while officially a Lieutenant Commander, is almost certainly not a Line Officer but a ranking specialist. In the given situation, Ensign Ro would almost certainly be the ranking line officer on the bridge until someone of higher rank was found.
To quote the wiki entry
Within combat units, line officers are in the chain of command, but officers in specialist fields (such as medical, dental, legal, supply and chaplain) are not, except within their own specialty. For example, a medical officer in an infantry battalion would be responsible for the combat medics in that unit, but would not be eligible to command the battalion or any of its subordinate units.
As noted above, though the Enterprise may not be considered, strictly speaking, a combat vessel, it can, as an exploratory vessel, find itself in combat at any point, and would almost certainly retain this element of modern organizational structure, or some variant thereof. Such manner of which system would almost certainly not place an untaught, command-inexperienced officer, such as Troi, in charge instead of a trained line officer such as Ro. The difference in rank is irrelevant. The granting of officer rank in line of command means you are expected to be able to perform at least the basic duties of such, even if a mere ensign. Ro, especially due to her inexperience, would also be expected to lean heavily on a mature and highly experienced chief petty officer (the naval equivalent to an army sergeant) such as Chief O'Brien, given his presence and wide experience. The final decisions would be hers, but he would be the one giving advice and counsel as to how best to proceed.