There's nothing wron with the .223/5.56. I don't know if you've seen the news lately, but it's getting all kinds of on-the-job-testing lately. You do have a good reason for going with a .308 AR, since you already have a .308. That's your main question now. Do you want another caliber, that will be different than what you currently shoot?
I can be patient and find .223 ammo for $6.50 per 20. Probably better if I REALLY looked, but after shooting .300 RUM for a while, I pretty much grabbed a case and ran, then sat in the closet holding my case of ammunition and laughed maniacally at the fools that sold my precious so cheaply. Well, ok, maybe not. But for going to a range and having a long session of very cost effective fun, .223 and 9mm aren't bad calibers to have in your bag of tricks.
To Sum up: It's used for different purposes. It's probably at least an order of magnitude cheaper. You can shoot more, cheaper, for less wear and tear on your shoulder, longer. But you'd have to buy more reloading dies. And maybe powder. And probably primers. And bullets.