I don't think it a case of one 'winning' they are totally different materials that have their own strengths and weaknesses.
Generally wood (balsa ply spruce etc) makes for a stiffer airframe especially at larger sizes. Stiff is god for flying characteristics because you get a crisper responding plane. But when it comes to absorbing an impact stiff can be bad. In a heavy crash balsa/ply tends to shatter potentially making repair impractical or at least very time consuming.
Foam on the other hand absorbs the energy of an impact by compressing and flexing, so damage tends to be less catastrophic and more easily fixed.
But yeah, foam models do tend to start to look shabby after a while due to hanger rash etc, whereas balsa models (providing they aren't crashed) can look good for years. Though to be fair I've seen plenty of very ratty balsa model too!
Personally I also much prefer balsa mainly because balsa models feel like a craftsman made product, built by human hand with skill and care. Something you can feel proud of. Foam models are just spat out of some giant machine, no different to the foam packing in your new microwave oven.