For a carbine build.
What barrel is the better option and why??
16 inch White Oak
16 inch Daniel Defense
16 inch BCM
I know White Oak is not chrome lined. Leaning toward the DD but not really sure, at one point leaned toward the White Oak, but again not really sure. These barrels will be for a build that I’m doing.
I would avoid White Oak for a couple of reasons.
As you mentioned, its not chrome lined. Chrome lined barrels are less accurate that non CL barrels, but CL barrels are much easier to clean and maintain. CL barrels also last longer.
They are chambered for .223. This is not necessarily a bad thing, but a true 5.56 NATO chamber is recommended because you can shoot both 5.56 NATO and .223 (the inverse is not true because of the higher pressure 5.56 NATO ammunition generates).
BCM and DD are both great choices.
Also keep in mind rate of twist and gas system length.
Avoid none chromed barrels.
C4
Agreed with all of the above. I would also consider what twist rate works best for you. My understanding is that a 1 in 7 is desirable as it allows use of a wider range of bullet weights.
Either of these. Which one you choose really depends on the configuration you want as far as profile, gas system length, etc.
I suspect you’ll get a similar response from just about everyone on this website.
white oak not chrome lined? i’m confused… did WOA start making chromoly barrels while i wasn’t looking? white oak barrels aren’t chrome-lined because they’re stainless steel. you don’t chrome line stainless steel, and you don’t use stainless when you’re wanting chromoly… likewise, you don’t use chromoly when you’re wanting stainless… one’s for high-durability, the other’s for high-accuracy. you don’t usually get both from one barrel.
so if you’re wanting a shoot-the-shit-out-of-it carbine, WOA (white oak armament) shouldn’t even be on the list. if you’re building more of a “recce” style, higher accuracy 16" weapon, then WOA is a great option.
also, WOA isn’t chambered for .223 unless you’re getting their “match” barrels… most of their barrels are Wylde chambered, which is good to go for precision fightin’ guns.
Chrome lining was just the answer to the problem of the barrel overheating, wasn’t it? In full auto mode, the barrel would overheat and foul causing a round to get stuck in the chamber. The result was the bolt ripping off the back of the cartridge leaving a brass ring inside the chamber, rendering the rile useless, except a heavy stick. Chrome Molly sleeves were later added to reduce the amount of heat and fouling thus reducing occurrences of this issue. Though I saw this on weaponology, so I could be talking out my ass! 
Chrome lining prevents corrosion in the chamber from sealing a case in the chamber and reduces the effects of fouling during firing.
It has very little (if anything) to do with overheating.
ADCO just came out with a new barrel. Mid length, CL, CMV, med weight, 16", 5.56 chamber, 1/7". You can get it naked or in a dissy setup.
http://www.adcofirearms.com/itemdetails_.cfm?inventorynumber=3622
Rumor has it they’re manufactured by White Oak to ADCO’s specs, but you’d have to verify that.
I agree with everything bkb0000 posted above. It really depends on your intended application for the firearm. White Oaks produces some very nice precision barrels.
+1
WOA barrels are magic!
What weight/profile are you considering? LW, Govt, mid-weight?
I would look at getting a “Daniel Defense” CHF 16 inch, chrome lined, mid-length gas, in a lightweight (.625") barrel profile. IMHO this maybe the best all around barrel configuration for the AR15/M16 rifles. You may want to contact Daniel Defense or G&R Tactical to find out when these barrels will be available.