I only have a little over a year's worth of experience with stainless and synthetics while I have several decades worth with wood and blue. So, I can't give you a great deal of real world advice to help with your decision. I can tell you why the last two rifles I purchased were stainless/synthetic, however.
I am probably more conscientious than most when it comes to maintaining firearms, so you won't likely find rust or damaged wood on any of my rifles. However, I have found that it takes a lot of time and energy to keep them in top shape. This is the main reason that I have started buying stainless and synthetics -- less upkeep.
With stainless (which, like any steel, is susceptible to corrosion) I don't have to worry about the finish (bluing) wearing away or showing scratches. I just keep it clean and oiled -- it just keeps looking like it did when new.
With synthetics stocks, I don't worry about soaking rains warping them, or about oil seeping into their grain to make them spongy. They just keep taking whatever comes along without cracking or warping or whatever. They aren't as aesthetically pleasing as many of the wood stocks out there, but they are functional and dependable. I'm really liking them, so far.
Regards,
jbgood