Hi Jasmine
That is a really hard question to answer because we ended up loving both resorts

As far as which resort has the better overall concierge, hands down I have to say the Polynesian. When I think of all the things I liked about the Wilderness Lodge and the concierge there, MOST of it has to do with the resort itself and NOT really anything to do with the concierge part of it. But at the Polynesian, there were a lot of things that made the concierge building, view, lounge, etc, VERY special
So, basing my answer on concierge VS concierge, I'd have to say the Polynesian! But to choose based on the resort itself, it's too hard to decide. A lot of things would factor in, if I were choosing where to stay again for an anniversary.
I LOVED the fact that the Polynesian concierge was able to get the cake for me from the Grand Floridian (I actually ordered it myself, but they handled picking it up and making sure that it got to 'Ohana that night and was delivered to our table per my wishes). Then again, maybe the WL concierge would've been able to do this too, just not sure! We really loved the feeling and atmosphere at the WL, but then again, we loved the feeling and atmosphere of the Polynesian!
Ok, after all this thinking out loud, I have to say, I'd choose the Polynesian resort over the WL. But by a *very* small margin!