It depends on if its an indoor or outdoor set up. Gas is more convenient for indoor use, with less work involved for daily operations, and depending on your location, can have the advantage of being more cost effective, if your paying cash expenses out of pocket for the fuel cost. The time needed, availability of optimal wood species, and or cost of wood needed, are things to weigh when dealing with wood burning appliances. You also have the work and extra time involved with daily operations of wood fired appliances, requiring time to build the fire and heat up before use. The fire building, and heating up can sometimes take an hour, as optimal operation is with a bed of coals, and one must maintain that bed of coals to keep the oven at optimal temperature throughout cooking operations. If your not familiar with fire operated appliances, and fire science, there can be a learning curve. Appliances that use alot of wood, sometimes leaves the users searching farther and farther, for that adequate wood supply, making efficient gathering of wood much more difficult. The type of wood, and the flavor imparted on your foods, is also something to consider. Some wood smokes have less then desirable flavors, while others are quite sought after. So these are all things relevant to your unique and individual circumstances, you will have to personally weight.
If its feasible to have both as an option, with gas for indoor, and wood fired for outdoor. That may give you the best of both worlds, and an option to put the heat where its most efficient in that season.
Don't count your weasels before they've popped. And now for a mulberry bush related tiny ad: