A lot depends on where you'll be backpacking. In the western US, fires are often banned altogether during the dry season because of the forest fire danger. In some cases, alcohol stoves (or any other stove without an on-off valve) are banned, too. Wood fires are also usually banned at timberline and above due to the scarcity of fuel. Of course that's not a problem where you live!

The other issue with wood fires is that they definitely soot up the outside of your cooking pot. IMHO this isn't a big deal as long as nothing rubs against it. You'll want to have a solid (not mesh) stuff sack for it to keep the soot from rubbing off on everything inside your pack.

I myself prefer a canister stove (mine is a Primus Micron) for its convenience and because I regularly backpack where wood fires are discouraged or forbidden.