I'm sure this has been covered a lot but I couldn't find the answer I am looking for. Which barrel will shoot 556 more accurately, 223 wylde or 556?

Theoretically the wylde chamber will be more accurate when shooting quality 223 ammo.  Most wylde chambered barrels are stainless as well if that's a concern of yours.

Yes it's been covered ad nausium.

http://www.ar15.com/forums/t_3_12/664199_Any_reason_NOT_to_go_with_a__223_Wylde_chamber_.html#i6708285

https://www.ar15.com/forums/t_3_66/690191_.html#i7106803

http://www.ar15.com/forums/t_3_4/613941_some__223_wylde_questions.html#i6050607

https://www.ar15.com/forums/t_3_12/706724_-223-Wylde-Chamber-More-Reliable-than-5-56-NATO.html#i7344550

Here is the question. Are you making a genuine benchrest/target only precision rifle? If so, buy a quality barrel with a Wylde chamber, and make holes in targets.

I'll point and facepalm when you come back after trying to use said rifle as a home defense firearm or range blaster toy and discover that you can't eject live rounds when loaded up with cheap 55gr FMJ.

Unless you are handloading precision loads, using a high quality made blank and barrel, in a well built rifle, it's unlikely you would ever be able to tell any difference between a Wylde chamber and a larger mil type chamber.

If you are looking for a general purpose, general use rifle, my advice is to leave the Wylde chamber to the benchrest and service match folks.

OP:  Are you going to shoot match ammo?  Real sub MOA match ammo?  Are you a good enough shot to shoot sub MOA with that ammo?  Is your rifle otherwise set up for sub MOA shooting, such as match/target trigger and suitable scope?  If your honest answer to ANY of these questions is "no", then a Wylde chamber is a waste.

I have not had any problems with my Wylde chambers, but I have seen a few negative posts.
I only use ammo that I know from previous experience is GTG.
Also I check headspace; you might be surprised at how many barrels are a little tight with some bolts.

I own several 5.56 barrels: BCM, Noveske as well as a few 223 wylde: BA, Rainer, Faxcon.  They all shoot both 223 and 5.56 well.

My Ballistic Advantage Wylde ran fine with some plinking 55 gr 5.56 reloads.

Now to work up a good 62 gr load.

All 3 of my barrels so far have been 223 Wylde and I have never had an issue with them - always been 100% reliable. They've been fed a steady diet of Wolf Gold over the years without a hiccup. I have my first Faxon barrel on the way with a 5.56 chamber, so I'm curious to see if I notice anything different in the accuracy department, but I'm not expecting to.