What would help me decide between a wood replacement window and a vinyl replacement window?

The differences here are many. Vinyl windows are generally inexpensive replacements for wood or other materials, while wood windows are designed for beauty and longer-term, more energy-efficient installations. 

Vinyl Windows

Vinyl windows cannot be painted or stained to match the look of the house, but they are also "no-maintenance." However, vinyl windows will not look like the wood frame windows you're replacing, and that can be a serious flaw for some. In very hot and cold climates, the expansion and contraction of vinyl windows can cause the pane to separate from the frame and create issues with leaking.

Wood Frame Windows

Architects almost always use wood-frame windows for performance and aesthetic reasons. They are, however, more expensive than vinyl windows and also require more maintenance. A wood window will rot and the paint will peel, though exterior-clad versions significantly reduce this risk. Often, the cladding is made of aluminum with a baked-on finish. Perhaps most importantly with the advent of energy efficiency is that wood windows tend to be better insulators than vinyl.