Well I might be a bit biased, but not as much as you'd think.
In order to compare the 2 you have to generalize, and each individual design has thier advantages and disadvantages. I've seen composite planes take longer to build than wood, and seen very light and rugged construction out of composites, so it gets muddy in those waters....
It comes down to what you want. If you're in a hurry, don't build a wood kit

but if you have time and enjoy the process, it's very rewarding. Wood planes can be lighter and stiffer given the same weight and design, but the drawback is again it takes more work from you.
I have to say in my personal experience a wood plane is infinitely more durable in a glow set up than a composite plane, as far as longevity. Electric is a different story, they are about the same. But long term vibration can wreak havoc on a composite plane....that's being very general, and it depends on the construction.
Composite planes are generally faster to build, easier to produce in mass, and much more resistant to dings and dents. You can also get some really cool shapes and curves that aren't generally possible with a wood plane, unless you're a master builder.
Wood planes are easier to repair, generally speaking. There's not much you can't fix with a wood plane. They are also much easier to modify or change, and that's why prototypes are generally wood unless you have a fully staffed factory. Once a mold is made, people are reluctant to scrap it even if it's wrong.
As mentioned wood planes have a different harmonic and do absorb noise a little differently. This probably only matters with a glow plane.
Wood fuses tend to be much stiffer and don't flex under loads. Want to try something to make you drop a jaw? Do a knife edge loop in close. Take good quality video. Now go back and slow that video down durning that last 1/4 loop. That air is doing nasty things to the airplane. Most composite planes are twisting the living hell out of that tail section. A stiff wood plane doesn't do it. Again it totally depends on the design, but you will be shocked at what's going on. Also listen closely, you can HEAR it...the air going nuts as it transitions the loads over that fuselage.
The one construction type that seems immune to this is nomex, as long as extra care is taken on the seam to stiffen it. TAVS is the worst at this, and a fully boxed and cross braced balsa fuse is one of the best. What does it matter? Not sure. Just interesting and I'm glad my plane doesn't do it LOL!!!
Some of the best construction in the ARF world is done by Oxai. they have found the best of both worlds, using balsa molded into shapes with composite skins. Generally speaking they are very light and beautiful, but can be fragile. They are also expensive by most people's standards. But there is no question that they are worth the money, especially if you don't really have the time or desire to build.
I like to think we've made great strides in simplifying construction on the wood planes so it's not as painful as the "old days". But there's no way around the finish process, and that can make or break the plane. Myself and Dean Funk have gone to great lengths to detail the process so anyone can be successful doing it, but there's X amount of work to be done and it's unavoidable. Unless you enjoy it, that's a down side.
Now as far as flying? Totally depends on the design and the pilot's trimming abilities. There are some awesome designs out there right now, with more on the way, in all areas. So no matter what you choose construction-wise, you're not giving anything up as long as you do your homework.
Cost wise? Welp, that REALLY depends on you. Yeah you can get in a wood plane slightly cheaper than a composite plane, but you have to be very picky with your equipment and you pay in work. one way or another, a good pattern plane costs you. In time or money, or both. There are some really good flying "middle of the pack" composite planes that cost between $1000-$2000 and these are probably the best selling and most popular planes in pattern, in the USA. They fly well when trimmed, and if you take care of them you can get a few seasons out of them. If you are ever watchful you can get many years out of them. Quality control and weight seem to be a bit iffy with these, but again if you do your homework, and ask the right questions to the right people, you can find out what's what and get set up with a very good plane. if you get antsy and choose poorly, you will get a heavy crooked abortion. but this is not as common as it was in years past, as all manufacturers are doing a much better job.
The last thing to mention is availability. This one can be HUGE. When composite plane manufacturing and delivery is in full swing, you can get it like right now. but be smart and pick up a spare chin cowl and canopy because down the road, you might be hard pressed to find one. These planes are usually made overseas in runs and when they're gone, they're gone. Again ask questions because some are better than others. but know how much replacement parts cost, lead time on getting them, and if they will be available down the road.
There are some wood planes made in the US. But as one of the makers of these, let me tell you how that goes. We're all cottage industries, every last one of us. We do everything we can to keep lead times down and do what we can for you. But sometimes life rares up and throws us a curve ball. And if we have to handle it, that leaves nobody else to make the stuff and TCB. None of us are rich, and we do it because we love it....and nothing more. Sometimes it feels like more of a hassle than it's worth. but I just love it too much. So my point is just understand that we're not some huge company with endless resources and people on the payroll, it's just us. but we're making great strides and doing really awesome things. And I'm proud to be a part of it.
Well I hope that answered some questions. if you have any specifics, ask away and someone will have an opinion (answer is such a relative term LOL). As for me, I like my woodies...I'm biased. But my planes are the definition of composite, I use balsa, foam, plywood, carbon, phenolic, fiberglass, kevlar, everything. All materials have thier strengths and weaknesses.
-Mike