Perhaps Sailing Instructor has something there, although it still strikes me that it's like asking whether arms or legs are more important to a person.
Of course, fundamentally what is a Navy but a collection of personnel who serve in and support a number of ships? So clearly equipment and personnel are critical. Put that way, customs and traditions seem by definition to take third place. But I'd argue that they are an essential element in a healthynavy, and are ignored and/or messed with willy-nilly to the cost of morale, esprit de corps, and therfore ultimately, fighting efficiency.
I joined the Navy about a quarter of a century ago (my bones creek as I type), in the dark days of "rust out". We did a great deal with what we had, but it was embarrassing internationally to show up with our 3"50 guns and Mark 10 mortars in the age of missiles. It was heart-breaking, and I'd hate to see us go back to a situation like that regarding equipment. Besides which, if we are potentially going to send our sailors into harm's way, they deserve the best equipment that can be provided.
The way we treat our personnel has greatly improved over the last couple decades as well. But if we hope to attract and retain good people, we need good personnel policies. Otherwise, every time the economy improves, a lot of people will jump ship and go back to the private sector.
To answer the question then, I reckon I'm siding with the order: equipment, personnel, traditions. But I wouldn't want to be in a Navy that didn't place a strong emphasis on all three.