More reliable due to it's loose tolerances. Either weapon in my experience will function perfectly in ideal settings, but with my AR I would get some problems if the bolt got too hot and wasn't given time to cool down. Heat wasn't an issue with my WASR.
What are you considering to be "more reliable?" Generally today's AR's are more reliable than AK's when the user has the ability to properly clean and lube the gun. AR's still get a bad rap due to botched decisions during its early use. The only semi-legitimate issue is the relative durability (lack thereof) of GI magazines which is by and large a non-issue for stateside owners and easily remedied with PMags anyway.
I don't know what your experience is with AKs, but I haven't been able to perform any better with an AR than with an AK at 50-100 yards or so. As I said above, this is all from my personal experience. I don't shoot rifles more than 3-4 times a year compared to handgun shooting which I get a lot more practice with (I enjoy it more).
What are you calling a "significant advantage" in terms of accuracy? Average off the shelf AR can easily get 1-2 MOA. Average off the shelf AK is doing good to hit 5 MOA. That's a pretty significant accuracy advantage if you ask me. I guess if you're talking about defensive shooting at 25 yards or less, ya, the AR doesn't have a "significant advantage." But you know what 25 yards is in terms of defensive shooting? Buckshot range.