I shot recurves from the mid 1960's to about 1980. Shot compounds from early '80's to mid '90's. Back to recurves from mid '90's to now. Compounds potentially have greater accuracy at longer yardage because of arrow speed and sights. Well tuned compounds will easily shoot a hunting arrow more than 400 yards. A well tuned recurve won't shoot quite 400 yards (unless you are really strong). Either type bow, well tuned, is more than adequate in both speed and accuracy to harvest any game in North America at reasonable yardage.
The accuracy question is a personal thing. Some people work with compounds enough that they can consistently shoot a 2" five shot group at 50 yards. Some people shoot recurves enough that they can consistently shoot 5" five shot groups at 50 yards. The question is, are you willing to do the practice necessary to master a recurve at that range. Of course, the shorter the yardage, the more likely you are to hit the target.
At reasonable hunting yardages, say up to 40 yards, either bow is adequate. At longer ranges, some lighter weight recurves might not have the energy to take down really big game.
The typical problems with compounds: (1) the never ending tinkering with accessories and addition of new or better gadgets/accessories -- always costs more money (2) since it is easier to make accurate shots with sights and arrows shoot pretty flat from 20 to 60 yards, many hunters will take shots way longer than they should (3) if something on the bow, one of the gadgets or accessories comes loose or breaks, your hunt is probably over (4) requires special tools and presses to maintain (5) the primary skill you must master is pulling the string back to the same place every time -- everything else is the bow and gadgets.
Typical problems with recurves: (1) you have the stick and string, might change the serving on the string occasionally, might put a new shelf or strike plate carpet on occasionally, might put new silencers on the string occasionally -- most people son't shoot enough to wear out any of these things (2) many hunters don't practice enough to be very competent, so chances are most shots are out of their range -- practice with a recurve is absolutely necessary, and yes, every day is good (3) the only thing likely to ever go wrong is cutting your string (4) a takedown requires an allen wrench, they all require a stringer (string with pockets on end) at some point (5) instinctive shooting requires practice, hand eye coordination and memory -- no help from mechanical aids. Of course, you could put sights on a recurve or longbow.
If you just want to shoot good enough to hunt deer a few times each year, get a compound. If you enjoy archery and want to have fun shooting every day, go with a recurve or longbow. I personally prefer recurves.
You can't shoot wood arrows with a compound. You can shoot pretty much anything with a recurve. I personally haven't shot a wooden arrow since the 1970's. Why in the world would you mess with wood when there are so many amazingly accurate and durable arrows availabe now.
People who don't practice enough with either type bow will probably tell you extreme accuracy is not possible. People who attain extreme accuracy levels with either bow will probably not post in any accuracy blogs.