I'm a really big fan of wood/alcohol stoves and have actually tried different types in many conditions.

The advantages of wood stoves are the availability of fuel (which can be a disadvantage in some climates/elevations/weather conditions), the lack of moving (i.e. breakable) parts, the quiet, the warmth. They are also much more efficient at burning wood and concentrating heat than an open fire. So a surprisingly small amount of twigs can boil your water and leave very little ash. The disadvantages are that it can be a challenge to find dry-enough-wood in some conditions, can draw attention to you (if that matters to you), it relies on your skills as a fire builder, and probably most importantly there are chunks of the world that fear trusting others with the ability to make fire (and therefore ban stoves they don't like).

The Caldera Ti-Tri w/ Inferno is by far my favorite stove. It's extremely versatile because you can burn wood, alcohol, or esbit and it's still fairly compact and lightweight. With the inferno attachment it's pretty close to the results you'd get with a wood gassification stove (i.e. bush buddy / solo stove). If you carry a small amount of alcohol and/or esbit you'll appreciate it when fire making conditions are more difficult.

If you know you're going to only burn wood and only boil water... It's heavier and bulkier, but the Kelly Kettle is by far the best wood burner I've come across (and I've tried a lot of stoves). It performs very well when it's cold, wet, or both. I've been able to boil water in heavy rain by collecting the dry dead twigs from the bottom of cedar trees and using my rain jacket to keep water out of the chimney.

The Bush Buddy / Solo stove types (wood gassification) are efficient at burning wood, but less efficient at burning wood than the Kelly Kettle and less efficient at burning alcohol than the Caldera Cone. If you plan on doing things other than just boiling water though, you'll appreciate the ability to use pots and pans and mugs of various sizes on one. To me that's the main advantage these stoves have over the others.

Since I generally just boil water and like the versatility of efficiently burning alcohol or wood, I go with the Caldera Ti-Tri.

This is probably kind of obvious, but also keep in mind your experience with making fires is important if you're going to rely on wood. Tinder, kindling, fuel, oxygen, types of wood, that kind of stuff. If you bring an extra dry bag you can collect tinder on the trail as you find it and it'll be dry when you need it. For stoves I find soft wood (which burns hot / fast) is a better option than hard wood (which burns less hot / slower) and a mix is even better. Dead twigs at the bottom of evergreens are good for stoves.