Electronegativity trends: Is it more important to prioritize families or periods?
There's no hard and fast rule.  In fact, there's actually no rule per se that states that electronegativity does increase along the periods and decreases down the groups.  It's just a general trend, which can be and is broken on occasion.  For instance, Zinc, to the right of Copper, has an electronegativity of 1.66, while copper is 1.75, which "breaks" the rule that electronegativity increases along the periods.

As far as which one takes precedence, it's a case by case scenario.  In some cases, down one and right one would be very close, like you guessed, as with Scandium (1.20) and Zirconium (1.22).  However, if you go over to the non-metals, some of them increase radically in a down-one-right-one scenario (particularly from 3rd period to 4th period, such as Aluminum [1.47] to Germanium [2.02], Phosphorus [2.06] to Selenium [2.48], etc.), while some of them decrease radically (particularly from 2nd to 3rd period and 4th to 5th, such as Boron to Silicon, Oxygen to Chlorine, Arsenic to Tellurium, etc.)

Bottom line:  There's no rule.  You just have to either learn them by heart or check a periodic table such as this one: